Percentage
69 solved SSC CGL Quantitative Aptitude previous year questions on Percentage, each with the correct answer and a full explanation.
Q1
A student has to secure 35% marks to pass in a subject. If he gets 82 and fails by 23 marks. What is the maximum marks of the subject?
✓ Correct answer: a) 300
ExplanationLet maximum marks = 100a According to question Passing marks = Maximum Marks = Hence, Option A is the correct answer.
Q2
Raman spends 80% of his income. If his income is increased by 25% and the expenditure increase by 10%, then what will be the percentage increase in his savings?
✓ Correct answer: d) 85
ExplanationLet, Income of Ram = Rs 100a According to the question, Expenditure = 80a Savings = 100a – 80a = 20a If income increased by 25% Then, New income = And expenditure is increased by 10% New expenditure = New savings = 125a – 88a = 37a Difference in savings = 37a – 20a = 17a Required Percentage = Hence, Option D is the correct answer.
Q3
The present population of a town is 26010. It increases annually at the rate of 2%. What was the population of town 2 years ago?
✓ Correct answer: a) 25000
ExplanationLet, the population of the town 2 years ago is x. According to the question, Hence, Option A is the correct answer.
Q4
If the radius of the cylinder is increased by 25%, then by how much percent the height must be reduced, so that the volume of the cylinder remains same?
✓ Correct answer: a) 36
ExplanationLet, Initial radius = a, initial height = h, and final height = H According to the question, the radius increased by 25 % Final radius = a+a =1.25a Volume is same So, Initial Volume = Final Volume h= H=(0.64)h Difference in height = h – 0.64h = 0.36h Required decrease Percentage of height = [0.36h/h] 100=36 % Hence, Option A is the correct answer.
Q5
In an examination 65% students pass in history and 55% students pass in hindi. If 5% students failed in both the subjects, then what is the percentage of students who have passed in both the subjects?
✓ Correct answer: a) 25
ExplanationLet, Total students = 100 According to question Students passed in history only = =65 Students failed in history = 100 – 65 = 35 Students passed in hindi = =55 Students failed in hindi = 100 – 55 = 45 Students failed in both subjects = = 5 Students failed in at least one subject = 35 + 45 – 5 = 75 Students passed in both the subjects = 100 – 75 = 25 Hence, Option A is the correct answer.
Q6
A solid cone of height 24 cm and radius of its base 8 cm is melted to form a solid cylinder of radius 6 cm and height 6 cm. In the whole process what percent of material is wasted?
✓ Correct answer: c) 57.8
ExplanationVolume of cone = × × = × × = 512 Volume of cylinder = × = × = 216 ∴ % of material wasted = × 100 = × 100 = 57.81 % Hence, Option C is the correct answer.
Q7
A man wills 25% of his wealth to charity and rest to his family. What percent of the wealth willed to charity does the family get?
✓ Correct answer: c) 300
ExplanationLet, total wealth = 100a According to the question, Wealth to charity = Wealth to family = Required percentage = Hence, Option C is the correct answer.
Q8
Sudha saves 15 % of her income. If her expenditure increases by 20 % and savings increase by 60 %, then by what percent has her income increased?
✓ Correct answer: a) 26
ExplanationLet, Rs.100 be the income.Then, saving = Rs,15 and expenditure =Rs, 85 Newl expenditure(Rs) = New saving(Rs) = Income increased % = (102+24) -100 = 126 -100 = 26 Hence, Option A is the correct answer.
Q9
The price of sugar is increased by 17 %. A person wants to increase his expenditure by 8 % only. By what percent should he decrease his consumption, nearest to one decimal place?
✓ Correct answer: d) 7.7 %
ExplanationLet, the cost price of sugar Rs. 100 The price of sugar is increased by 17 % As per the question, Price of sugar after increased = = 117 But person wants to increase his expenditure by 8 % So his expenditure = = 108 Required Percentage = = 7.69 = 7.7 % Hence, Option D is the correct answer.
Q10
The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?
✓ Correct answer: a) 10.3
ExplanationLet, the initial price of the sugar is Rs. 100x.Price increased=17% New price of the sugar =100x+100x×17%=Rs.117x Also let initial expenditure of the sugar is Rs.100y.Expenditure increased=5% New expenditure=100y+100y×5%=Rs.105y Intial consumption= New consumption= Required percentage Hence, Option A is the correct answer.
Q11
The price of sugar is increased by 22 %. A person wants to increase his expenditure by 12 % only. By what percent should he decrease his consumption, nearest to one decimal place?
✓ Correct answer: c) 8.2 %
ExplanationLet, the cost price = Rs.100 As per the question, Increased price = Rs.122 But the person wants to increase his expenditure by 12 % only, So, Let he decrease his consumption x %, 112 = 122 × (1- ) x = 8.19672 % x = 8.2 % Hence, Option C is the correct answer.
Q12
The price of sugar is increased by 24 %. A person wants to increase his expenditure by 15 % only. By what percentage, correct to one decimal place, should he reduce his consumption?
✓ Correct answer: a) 7.3
ExplanationLet initial price of the sugar is Rs. 100x .Price increased=24% New price of the sugar =100x+100x×24%=Rs.124x Also let initial expenditure of the sugar is Rs.100y .Expenditure increased=15% New expenditure=100y+100y×15%=Rs.115y Intial consumption= New consumption= Required percentage Hence, Option A is the correct answer.
Q13
The price of sugar is increased by 17 %. A person wants to increase his expenditure by 7 % only. By what percentage (correct to one decimal place) should he reduce his consumption?
✓ Correct answer: c) 8.5 %
ExplanationThe price of sugar is increased by 17 %.A person wants to increase his expenditure by 7 % only.Expenditure = Price × consumption Expenditure = 100x × 100y Expenditure = 10000xy As per the question, New expenditure = New price × New consumption 10700xy = 117x × New consumption New consumption = 91.45y Percent reduce in consumption = % = 8.5% Hence, Option C is the correct answer.
Q14
While selling an article of marked price ₹ 5,040 at a discount of 40%, if a trader gains 20%, then the profit in ₹ is:
✓ Correct answer: b) ₹ 504
ExplanationGiven, Marked Price Discount Selling Price Profit Cost Price Profit Selling Price - Cost Price Hence, the correct option is B.
Q15
Two bottles of the same capacity are 35 % and 33 % full of orange juice, respectively. They are filled up completely with apple juice and then the contents of both bottles are emptied into another vessel. The percentage of apple juice in the mixture is:
✓ Correct answer: c) 65
ExplanationTwo bottles of the same capacity of orange juice = 35 % and 33 % Capacity of both vessels is the same the average percentage of orange juice percentage of apple juice = 100% - =
Q16
Lucky spends 85% of her income. If her expenditure increases by x%, savings increase by 60% and income increases by 26%, then what is the value of x?
✓ Correct answer: b) 20
ExplanationLucky spends 85% of her income.Let, the income of Lucky = 100 unit Expenditure of Lucky = Saving of Lucky = 100 unit – 85 unit = 15 unit If her income increase by 26% and expenditure increase by x percent then her saving also increases by 60%.Using : Expenditure + saving = income According to the question, Hence, Option B is the correct answer.
Q17
The total number of students in a school is 1400, out of which 35% of the students are girls and the rest are boys. If 80% of the boys and 90% of the girls passed in an annual examination, then the percentage of the students who failed is:
✓ Correct answer: a) 16.5
ExplanationNumber of girls in school = 1400 × = 490 Number of boys in school = 1400 – 490 = 910 Number of girls who failed in annual examination = = = 49 Number of boys who failed in annual examination = = = 182 Total number of students who failed in annual examination = 182 + 49 = 231 Therefore, required percentage = = 16.5% Hence, option A is correct
Q18
The present population of a village is 15280. If the number of males increases by 25% and the number of females increases by 15%, then the population will become 18428. The difference between present population of males and females in the village is:
✓ Correct answer: a) 1840
ExplanationThe present population of a village = 15280 Let, present population of male in village = x Present population of female in village = 15280 – x If the number of males increases by 25% and the number of females increases by 15%%, then the population will become 18428. According to the question, The present population of male in village = 8560 Present population of female in village = 15280 – 8560 = 6720 Difference between present population of males and females in the village = 8560 – 6720 = 1840 Hence, Option A is the correct answer.
Q19
Avinash has 20% less coins of different countries than Gaurav has. Gaurav has 40% more such coins than Chetan has. By what percent the number of coins which Chetan has is less than the number of coins which Avinash has? (correct to one decimal place)
✓ Correct answer: c) 10.7
ExplanationLet, Chetan has x coins Number of coins which Gaurav has = = = Number of coins which Avinash has = = = Therefore, required percentage = = = 10.7% Hence, Option C is the correct answer.
Q20
Price of a one gram gold coin decreased by 10% on its initial price on Monday and increased by 20% on Tuesday and again increased by 8% on Wednesday, and 5% increase on Thursday. If the final price on Thursday is ₹5511.24, then the initial price (in ₹) of one gram gold coin on Monday was?
✓ Correct answer: b) 4500
ExplanationThe price of a one gram gold coin decreased by 10% on its initial price on Monday and increased by 20% on Tuesday and again increased by 8% on Wednesday, and 5% increase on Thursday.The final price on Thursday is Rs.5511.24 Let, the initial price (in Rs.) of one gram gold coin on Monday = Rs. P According to the question, Hence, Option B is the correct answer.
Q21
Radha saves x% of her income. If her income increases by 28% and the expenditure increases by 20%, then her savings increase by 40%. What is the value of x?
✓ Correct answer: d) 40
ExplanationLet, the income of Radha = 100 unit Radha saves of her income.Saving of Radha = Expenditure of Radha = (100 – x) unit If her income by 28% and the expenditure increases by 20%, then her savings increase by 40%.Using : Income = Expenditure + Saving According to the question, x = 40 Hence, Option D is the correct answer.
Q22
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29% , then her savings increase by:
✓ Correct answer: d) 56%
ExplanationLet income of Radha = 100 unit Radha saves 25% of her income.Saving of Radha = Expenditure of Radha = 100 unit – 25 unit = 75 unit Now, Expenditure increases by 20% and her income increase by 29% New income = New Expenditure = New Saving = 129 unit – 90 unit = 39 unit Percentage increase in Radha’s saving = Hence, Option D is the correct answer.
Q23
Chamanlal, Arshad and Jagit Singh contested an election. All the votes polled were valid. Arshad got of the total votes. For every votes Chamanlal got 14 votes. The winner got 4950 more votes than the person who received the least number of votes. Find the total number of votes polled.
✓ Correct answer: d) 33000
ExplanationChamanlal, Arshad and Jagjit Singh contested an election.All the votes polled were valid.Arshad got 35% of the total votes.Let the total number of polled votes be 100. Total number of votes obtained by Arshad = For every 35 votes Chamanlal got 14 votes.For every 1 vote Chamanlal got votes For 100 votes Chamanlal got Total number of votes obtained by Chamanlal = 40 Now, Number of votes obtained by Jagjit Singh = 100 – 40 – 35 = 25 According to the question, 40 votes – 25 votes = 4950 15 votes = 4950 1 vote = 330 100 votes = 33000 Hence, the total number of votes polled = 33000 Hence, Option D is the correct answer.
Q24
In an examination, 45% of all the students who appeared are boys and the rest are girls. If 60% of the boys and 70% of the girls passed, then what is the percentage of students who failed?
✓ Correct answer: b) 34.5
ExplanationLet, the number of total students = 100x Number of boys who appeared in the examination = = 45x Number of girls who appeared in the examination = 100x – 45x = 55x Number of boys who failed in the examination = = = 18x Number of girls who failed in the examination = = = 16.5x Therefore, the percentage of students who failed in the examination = = = 34.5% Hence, Option B is the correct answer.
Q25
A sports-goods shop has tennis balls of 3 colors - red, green and white. The number of white balls is 60% more than the number of red balls and the number of green balls is 12.5% less than the number of white balls. If the total number of balls is 120, then how many green balls are there?
✓ Correct answer: d) 42
ExplanationA sports-goods shop has tennis balls of 3 colors – red, green and white.The number of white balls is 60% more than the number of red balls and the number of green balls is 12.5% less than the number of white balls.Total number of balls = 120 Let, the number of red balls = x Number of white balls = Number of green balls = Hence, Number of green balls = Hence, Option D is the correct answer.
Q26
The train ticket fare from places A to B in 2nd class AC and 3rd class AC is Rs. 2,500 and Rs.2,000, respectively. If the fares of 2nd class AC and 3rd class AC are increased by 20% and 10%, respectively, then find the ratio of the new fares of 2nd class AC and 3rd class AC.
✓ Correct answer: b) 15 : 11
ExplanationIncreased 2nd class AC fare = 2500 × 120% = Rs. 3000 Increased 3rd class AC fare = 2000 × 110% = Rs. 2200 Required Ratio = 3000 : 2200 = 15 : 11
Q27
The price of petrol shot up by 5 %. Before the hike, the price was ₹ 82 per litre. A man travels 3045 km every month and his car gives a mileage of 15 km per litre. What is the increase in the monthly expenditure (to the nearest ₹) on the man's travel due to the hike in the petrol prices?
✓ Correct answer: a) 832
ExplanationGiven, The price of petrol before hike is ₹82 The man travels 3045 km every month and his car gives a mileage of 15 km per litre.Total expenditure before hike = 82 × = Rs. 16,646 The increase in the monthly expenditure after hike = 16646 × ≈ Rs. 832. Hence, Option A is the correct answer.
Q28
In an election between two candidates, 12% of voters did not cast their votes. The winner by obtaining 68% of the total votes defeated his contestant by 2880 votes. What was the total number of voters who cast their votes in the election?
✓ Correct answer: a) 5280
ExplanationAccording to the question, ∴ The total number of voters who cast their votes in the election= 5,280 Hence, Option A is the correct answer.
Q29
Ankita's weight is 20 % less than that of her grandmother. The grandmother weighs 26 kg less than grandmother's husband, whose weight is 81 kg.If Ankita's brother is 8 kg heavier than Ankita, then what is the weight (in kg) of Anikita's brother?
✓ Correct answer: d) 52
ExplanationWeight of grandmother = 81 – 26 = 55 kg Ankita’s weight = = 44 kg Weight of Anikita's brother = 44 + 8 = 52 kg Hence, the correct answer is (D).
Q30
A number is decreased by to get another number. The number so obtained is increased by to get a third number. The difference of the third number and the original number is what percentage more or less than the difference of second and the third number?
✓ Correct answer: d) Less, 12.5 Percent
ExplanationLet the original number be 100. Then the number obtained by decreasing it by 20% is80. Then the number obtained by increasing 80 by 200% is 80 + 280 = 240 The difference between the third number and the original number is 240 - 100 = 140 The number obtained by decreasing 100 by 20% is80. The difference between the second and the third number is 240 - 80 = 160 Percentage change = = 12.5% Hence , the change is less than the original change by 12.5% The answer is Less, 12.5 Percent.
Q31
Anuja owns 66 % of a property. If 30% of the property that she owns is worth ` 1,25,000 then 45% of the value (in Rs.) of the property is:
✓ Correct answer: b) 2,81,250
ExplanationLet the total value of the property be 3x.Then, property owned by Anuja = (3x) × % = 2x 30% of Anuja’s property = Rs. 125000 Þ (2x) × 30% = 125000 Þ 0.6x = 125000 Þ x = = Now, total property = 3 × = Rs. 625000 So, 45% of the value of the property = 625000 × 45% = Rs. 281250
Q32
The reduction of 15 % in the price of salt enables a person to buy 2 kg more for ₹ 272. The reduced price of salt per kg (in ₹) is:
✓ Correct answer: a) 20.40
ExplanationThe reduction of 15% in the price of salt enables a person to buy 2 kg more for Rs. 272. Let Initial price of salt = 20x Final price of salt = 20x - = 17x If expenditure is constant then price is inversely proportional to consumption.Original price : Reduced price = 20x : 17x = 20 : 17 Original consumption : Reduced consumption = 17 : 20 Difference in the quantity consumed = 20 unit – 17 unit = 3 unit 3 unit = 2 kg 1 unit = kg Original consumption : Reduced consumption = kg : kg Reduced price of salt = Hence, the correct answer is (A).
Q33
Some students (only boys and girls) from different schools appeared for an Olympiad exam. 20 % of the boys and 15 % of the girls failed the exam. The number of boys who passed the exam was 70 more than that of the girls who passed the exam. A total of 90 students failed. Find the number of students that appeared for the exam.
✓ Correct answer: c) 500
ExplanationLet the number of boys be x and number of girls be y According to the question, 20x + 15y = 9000 4x + 3y = 1800 .....eq1 And, 80x – 85y = 7000 16x – 17y = 1400 x = By putting value of x in eq1 4 + 3y = 1800 29y = 7200 – 1400 29y = 5800 y = y = 200 By putting value of y in eq1 4x + 3 × 200 = 1800 4x = 1800 – 600 x = x = 300 Therefore, total number of students that appeared for the exam = 200 + 300 = 500 Hence, the correct answer is (C).
Q34
When the price of an item was reduced by 20%, its sale increased by x%. If there is an increase of 25% in receipt of the revenue, then the value of x is:
✓ Correct answer: d) 56.25
ExplanationLet the initial price be a and sale be b Then, revenue = ab According to question, Þ Þ 1600 + 16x = 2500 Þ 16x = 900 Þ x = 56.25 Hence, option D is the correct answer.
Q35
The selling price of 28 items is equal to the cost price of 17 items. What is the percentage of profit or loss?
✓ Correct answer: a) 39 % loss
ExplanationAccording to the given condition : Selling price of 28 article is equal to the cost price of 17 articles .Now , Hence, Option A is the correct answer.
Q36
The base of a triangle is increased by 40%. By what percentage (correct to two decimal places) should its height be increased so that the area increases by 60% ?
✓ Correct answer: a) 14.29%
ExplanationLet, the base and height of the triangle be 100x and 100y respectively.Area of the triangle = = New base = 100x + 40% of 100x = 140x New area triangle = 5000 xy + 60 % of 5000 xy = 8000 xy New height = Increase in height = % Increase in height = Hence, Option A is the correct answer.
Q37
A reduction of 20 % in the price of bananas enables a customer to buy 6 more bananas for ₹ 80 . What is the reduced price of bananas per dozen (in ₹)?
✓ Correct answer: a) 32
ExplanationPrice is reduced by 20% so he will save 20%.Saving = 20% of 80 = Rs. 16 Now he can buy 6 more bananas at the new price out of that savings.New Price per banana =Rs. New reduced price per dozen = × 12 = Rs. 32 Hence, the correct answer is (A).
Q38
Three candidates and participated in an election. got more votes than , and got more votes than . P overtook by 2,412 votes. If voters voted and no invalid or illegal votes were cast, then what was the number of voters in the voting list?
✓ Correct answer: a) 46,900
ExplanationLet, the number of voters in the voting list is 100 and Q got x votes.P got 35% more votes than Q. R got 15% more votes than Q. P = 1.35x R = 1.15x Out of 100 voters 90% voters voted. then, x + 1.35x + 1.15x = 100 of 90% x = P overtook R by 2,412 votes.(1.35x -1.15x) = 0.20x = Applying unitary method, Hence, the correct answer is (A).
Q39
A reduction of 15 % in the price of wheat enables a housewife to buy 6 kg more for ₹ 2,720. The reduced price of wheat per kg (in ₹) is:
✓ Correct answer: b) 68
ExplanationIf price becomes i.e., then the quantity will become of the original quantity.Increase in quantity = of the original quantity = of the original quantity of the original quantity = 6 kg So, the original quantity = 6 × = 34 kg New quantity = 34 + 6 = 40 kg Reduced price of wheat per kg = = Rs. 68 Hence, Option B is the correct answer.
Q40
A spends 65 % of his income. His income has increased by 20.1 % and the expenditure has increased by 20 %. By what percent (correct to one decimal place) does his saving increase or decrease?
✓ Correct answer: a) Increase by 20.3 %
ExplanationLet, income =Rs. 100 A spends 65 % of his income Expenditure= Rs. 65 Savings = (100-65)= Rs. 35 A.T.Q. Income : Expenditure: Savings= (120.1-78)= Rs. 42.1 Change in savings ⇒ Required % increase Hence, the correct answer is (A).
Q41
If the price of petrol is increased by 28%, by what percentage should the consumption be decreased by the consumer, if the expenditure on petrol remains unchanged? (Correct to 2 decimal places)
✓ Correct answer: b) 21.88%
ExplanationAccording to the given data : Ratio of price = 25 : 32 Ratio of consumption = 32 : 25 Hence, Option B is the correct answer.
Q42
The length and the breadth of a rectangle are made to increase and decrease, respectively, by 8 % and 10 %. What is the percentage increase or decrease in its area?
✓ Correct answer: d) Decrease by 2.8 %
ExplanationLet the length of the rectangle be l and breadth of the rectangle be b New length of the rectangle = = = 1.08 l New breadth of the rectangle = = = 0.90 b We know that: Area of the rectangle = length × breadth= lb New area of the rectangle = 1.08l × 0.90b = .972lb Therefore, percentage decrease = = = 2.8% Hence, the correct answer is (D).
Q43
In a manufacturing unit, it was noted that the price of raw material has increased by 25% and the labour cost has gone up from 30 % of the cost of raw material to 38 % of the cost of the raw material. What percentage of the consumption of raw material be reduced to keep the cost the same as that before the increase?
✓ Correct answer: c) 24.6 %
ExplanationLet price of raw material initially = 100 unit In a manufacturing unit, it was noted that the price of raw material has increased by 25%.Price of raw material finally = 100 unit + Also, the Labour cost has gone up from 30% of the cost of raw material to 38% of the cost of the raw material.Labour cost initially = Labour cost finally = Total cost initially = 100 unit + 30 unit = 130 unit Total cost finally = 125 unit + 47.5 unit = 172.5 unit We know that if expenditure is constant then cost is inversely proportional to the consumption.Now, percentage of the consumption of raw material be reduced to keep the cost the same as the before the increase = Hence, Option C is the correct answer.
Q44
In the election, 8% of the voters did not cast their votes. Two candidates contested the election, in which the winning candidate got 48% of the total votes and won the election by 1100 votes. Find the total number of voters in the election, given that all the votes cast were valid?
✓ Correct answer: c) 27500
ExplanationPercentage of invalid votes = 8% Percentage of votes received by the winning candidate = 48% Percentage of votes received by lossing candidate = 100 - (48 + 8) = 44% Difference = 48 - 44 = 4% Now, 4% = 1100 votes Hence, the correct answer is (C).
Q45
In a factory with 400 employees, the ratio of the number of male employees to that of female employees is 5 :3. There are 87.5% regular employees in the factory. If 92% of male employees are regular employees, then what is the percentage of regular female employees?
✓ Correct answer: a) 80%
ExplanationSol.Total number of employees in factory = 400 Number of male employees in factory = Number of female employees in factory = 400 – 250 = 150 Number of regular employees in factory = Number of regular male employees in factory = Number of regular female employees in factory = 350 – 230 = 120 Percentage of regular female employees = Hence, the correct answer is (A).
Q46
The price of an item is reduced by 20%. As a result, customers can get 2 kg more of it for Rs.360. Find the original price (in Rs.) per kg of the item.
✓ Correct answer: b) 45
ExplanationLet the original price be Rs. x/kg Reduced Price = x – 20% of x = Rs. 0.8x/kg ATQ, Hence, the correct answer is (B).
Q47
Raju, Ravi and Ashok contested an election. 5% votes polled were invalid. Raju got 30% of the total votes. Ravi got 32% of the total votes. The winner got 5136 more votes than the person who received the least number of votes. Find the total number of votes polled.
✓ Correct answer: a) 171200
ExplanationAccording to the given data , Ravi got 32 % of the total votes.Raju got 30 % of the total votes.Invalid votes = 5% Ashok got = (100 - 32 - 30 - 5)%= 33% of the total votes.Difference of Raju and Ashok = (33 - 30) = 3% So now, 3% =5136 1%= ∴ 100% = 171200 ∴ The total number of votes= 171200 Hence, Option A is the correct answer.
Q48
A person's salary was decreased by 50% and subsequently increased by 50%. By what much percent does his salary increase or decrease?
✓ Correct answer: d) Decrease 25%
ExplanationLet, the salary of man be Rs.100 After 50% decrease, new salary = 100 – 50 % of 100 = Rs.50 Again after 50% increase, new salary = 50 + 50% of 50 = Rs.75 Effective change in salary = Rs.100 – Rs.75 = Rs.25 % decrease in salary = = 25% Hence, option D is the correct answer.
Q49
In the first year the population of a town decreased by 5 % due to the Corona virus first wave. In the next year it decreased again by 5 % due to the second wave and in the third year it increased by 5 %. At the end of the third year the population was 9,47,625. What was the population at the beginning of the first year?
✓ Correct answer: b) 10,00,000
ExplanationLet's work through this step by step.We'll assume that the population at the beginning of the first year is .In the first year, the population decreased by 5%, which means it became of what it was at the beginning of the year: Population at the end of the first year = .In the second year, the population decreased again by 5%, which means it became of what it was at the end of the first year: Population at the end of the second year = .In the third year, the population increased by 5%, which means it became of what it was at the end of the second year: Population at the end of the third year = .According to the problem, the population at the end of the third year is given as 947,625: Now, we can solve for : Now, divide both sides by 0.947625 to find : So, the population at the beginning of the first year was 1,000,000. The answer is option B: 10,00,000.
Q50
In an election between two candidates, the defeated candidate secured 42% of the valid votes polled and lost the election by 7,68,400 votes. If 82,560 votes were declared invalid and 20% people did NOT cast their vote, then the invalid votes were what percentage of the votes which people did NOT cast?
✓ Correct answer: d) 6.8 %
ExplanationLet the total numbers of voters be P .So,total votes polled= Valid votes = votes got by the losers = 42% So, Votes got by the winner =100-42 = 58% Difference of percentage =(58-42) = 16% ATQ, Hence, the correct answer is (D).
Q51
In an election between two candidates, a candidate who gets of the total votes polled is elected by a majority of 1480 votes. What is the total number of votes polled?
✓ Correct answer: c) 2846
ExplanationIn an election winner got = 76% So, looser gain votes = 24% Difference between both = (76-24)% = 52 % Hence, the correct answer is (C).
Q52
In an election between three candidates, Arjun, Bhaskar and Saral contested for a post. Arjun got 50% votes more than Saral, and Saral got 2% votes less than Bhaskar. The difference between the votes of Bhaskar and Saral is 1296. What is the half of the difference between the votes of Arjun and Bhaskar?
✓ Correct answer: d) 15228
ExplanationLet, Bhaskar got 100x votes.So, Saral got = = 98x votes Arjun got = = 147x votes The difference between Bhaskar and Saral = (100x-98x) = 2x votes.The difference between Arjun and Bhaskar = (147x-100x) = 47x votes.According to the question, So, Half of the difference between the votes of Arjun and Bhaskar = 15288 votes Hence, Option D is the correct answer.
Q53
A basket contains 350 eggs. If 12% of the eggs are rotten, how many eggs are good enough to be sold?
✓ Correct answer: c) 308
ExplanationA basket contains 350 eggs.12% of eggs are rotten. ∴ The percentage of good eggs= (100 - 12)= 88% ∴ The number of good eggs= Hence, Option C is the correct answer.
Q54
Mrs. Deepa Devi saves 30% of her salary. If she receives Rs.42,000 per month as her salary, what is her monthly expenditure?
✓ Correct answer: b) Rs.29,400
ExplanationGiven, Mrs. Deepa Devi saves 30% of her salary.If she receives Rs.42,000 per month as her salary. ∴ The expenditure Hence, Option B is the correct answer.
Q55
In a constituency, 90% of the total number of people on the electoral roll cast their votes during an election. 15% of the votes cast were declared invalid. Jeeta secured 60% of the valid votes. If Jeeta secured 91,800 valid votes, what was the total number of people on the electoral roll?
✓ Correct answer: d) 200000
ExplanationLet, total number of people roll in the electoral list are x. Then according to question- So, the total number of people roll in electoral list are 200000. Hence, Option D is the correct answer.
Q56
In a constituency, 85% of the total number of people on the electoral roll cast their votes during an election. 10% of the votes cast were declared invalid. If there were 3,00,000 people on the electoral roll, and Dharam secured 1,37,700 valid votes, what percentage of the total number of valid votes did Dharam secure?
✓ Correct answer: d) 60.0%
ExplanationGiven, the total electoral roll = 300000 Now, according to the question, Total number of valid votes = Dharma got votes = 137700 Percentage of valid votes Dharma got = Hence, Option D is the correct answer.
Q57
In the first month, the income of Mohan increases by 30%. In the second month his income decreases by 30%. What will be percentage increase or decrease in the income after two months?
✓ Correct answer: d) 9% decrease
ExplanationLet the income be 100. then, New income = Income Percentage decrease = Hence, the correct option is D.
Q58
Rima spends 35% of her monthly income on food articles and 15% of the remaining on clothes. She saves 40% of the remaining income. If her monthly salary is ₹27,500, how much does she save (in ₹) every month?
✓ Correct answer: a) 6077.5
ExplanationMoney spend on food = 35% of 27,500 = 35 275 = ₹ 9625 Remaining money = 27,500 - 9,625 = ₹ 17,875 Money spend on clothes = 15% of 17,875 = 15 178.75 = ₹ 2681.25 Now,remaining money = 17,875 - 2681.25 = ₹ 15193.75 Amount of money he saves = 40% of 15193.75 = ₹ 6077.5 Hence, Option A is the correct answer.
Q59
Two candidates contested an election.One of them got 64% of the votes and won by 434 votes.What was the total number of votes polled?
✓ Correct answer: a) 1550
ExplanationIf one of the candidates gets 64% of votes. ∴ The other candidate gets (100 - 64)= 36% votes. ∴ The total number of votes polled= Hence, Option A is the correct answer.
Q60
Tarun owned a plot of land having an area that was 10% more than the area of the plot owned by Basab, while the area of the plot of land owned by Nakul was 40% more than the area of the plot owned by Tarun. If the area of the plot owned by Nakul was 2695 square feet, what was the area (in square feet) of the plot owned by Basab?
✓ Correct answer: a) 1750
ExplanationLet area of plot owned by Basab = 100 units Area of plot owned by Tarun = 100 units Area of plot owned by Nakul = 110 = 154units According to the given question, 154 units = 2695 square feet 100 units = square feet Therefore, Area of plot owned by Basab is 1750 square feet.Hence, The correct answer is (A).
Q61
In an election between two candidates, of the voters in the voter list did not cast their vote, whereas of the votes cast were found to be invalid. The winning candidate got of the valid votes and won the election by a margin of 1,458 votes. What is the total number of voters enrolled in the voter list?
✓ Correct answer: a) 15,000
ExplanationLet the total number of votes be T. Number of voters who did not cast their vote = 10% of T = 0.1T Number of voters who cast their vote = T - 0.1T = 0.9T Number of invalid votes = 10% of votes cast = 0.1 0.9T = 0.09T Number of valid votes = Total votes cast - Invalid votes = 0.9T - 0.09T = 0.81T Number of votes won by the winning candidate = 56% of valid votes = 0.56 0.81T = 0.4536T Winning margin = Votes won by the winning candidate - Votes won by the losing candidate So, the total number of voters enrolled in the voter list is approximately 15,000.
Q62
In January 2022, Kriti paid an EMI, which was 22 % of her monthly salary. She spent the remaining salary on shopping of groceries and clothes in the ratio 7:5. She spent Rs 18200 on shopping of clothes. If, in February 2022, her salary increased by 16 %, then what was her salary (in Rs) in February?
✓ Correct answer: d) 64960
ExplanationLet, total salary of Kirti was Rs. Now, she spent 22% of her salary on EMI and the remaining 78% on shopping of groceries and clothes.She spent Rs. 18,200 on shopping of clothes.5 units = Rs. 18,200 1 unit = Rs. 3,640 So, 12 units = Rs. 43,680 Now, Her salary, So, her salary in February = Hence, Option D is the correct answer.
Q63
The monthly income of a person was Rs. 80000 and his monthly expenditure was Rs. 45000. Next year, his income increased by 16% and his expenditure increased by 8%. Find the percentage increase in his savings.
✓ Correct answer: d) 26.29%
ExplanationWe know that, Saving = Income - Expenditure Initial saving = initial income - Initial expenditure = 80000 - 45000 = 35000 New saving = New income - New expenditure Percentage increase in savings Hence, option D is the correct answer.
Q64
A father gives of his monthly income to both his sons as pocket money. The elder son gets of the total amount given to both the sons. He spend of the amount and saves ₹ 17 . What is the monthly income of father?
✓ Correct answer: d) ₹2, 500
ExplanationLet the father's salary be Rs. x. Then part of salary given to the two sons as pocket money = Share of the elder son = Expenditure of the elder son = ∴ Savings of the elder son = Given, Hence, option D is correct
Q65
Ravi initially used to save 20% of his monthly income. Recently his monthly income was raised by 25%. His nominal savings also went up by 5%. What percentage of his present nominal income does Ravi currently save?
✓ Correct answer: b) 16.8 %
ExplanationLet us consider his salary to be Rs.100 Savings = 20% = Increase in salary = 25%= = Rs.25 New salary = 100 + 25 = Rs.125 Increase in savings = 5% = = Rs.1 New Savings = 20 + 1 = Rs.21 Percentage of his new saving to the new income = % Hence, the correct option is B.
Q66
While solving a division problem, Suhas by mistake took a number as dividend which was 10% less than the original dividend and he also took as divisor a number which was 20% less than the original divisor. If the correct quotient of the original question of division was 24 and the remainder was 0, then assuming that there was no error in his calculation, what was the quotient obtained by Suhas?
✓ Correct answer: a) 27
ExplanationLet correct dividend is x and correct divisor is y then, According to question- .......................(1) Now, Wrong dividend = And Wrong divisor = Then- Wrong quotient obtained = Hence, option A is correct
Q67
A family income is ₹ 35,000 in a month. The family spends the income on various expenditures, viz., food, health, education, entertainment, and rent. After incurring all the expenditures, 8 % is saved every month. The expenditure on health is 50 % more than that of food. While food is three times of the expenditure on entertainment, the expenditure on health is half of the expenditure on education. The expenditure on rent is one-third of the combined expenditure on food, health and education. How much expenditure in ₹ is incurred on education?
✓ Correct answer: a) 12600
ExplanationLet the expenditure on entertainment be 100x.Expenditure on food = 3 100x = 300x Expenditure on health = 150% of 300x = 450x Expenditure on education = 900x Ependiture on rent = one-third of (300x + 450x + 900x) = 550x Amount of money he saved = 8% of 35,000 = ₹ 2,800 As per the question 100x+ 300x+ 450x+ 900x+ 550x = 35000- 2800 2300x = 32,200 x = 14 Expenditure is incurred on education = 900x = 900 14 = ₹12,600 So,correct option is A.
Q68
Hari, Kamal and Lalit contested an election in which 6050 votes were polled and none of the votes were invalid. Kamal got 42% more votes than the total votes obtained by Hari and Lalit together. If Lalit obtained only 8% of the total polled votes, find the number of votes obtained by Hari.
✓ Correct answer: a) 2016
ExplanationVotes obtained by Lalit= 8% of 6050 Votes of Lalit= 0.08 x 6050 = 484 Let the votes obtained by Hari be H and by Kamal be K. According to the question, Kamal got 42% more votes than the total votes obtained by Hari and Lalit together.K=1.42 x (H + 484) Also, the total votes are the sum of votes of Hari, Kamal, and Lalit Substitute value of k Hence, Option A is the correct answer.
Q69
Sonu saves 15 % of her income. If her income increases by 20 % and she still saves the same amount as before, then what is the percentage increase in her expenditure? (correct to one decimal place)
✓ Correct answer: b) 23.5
ExplanationLet Initial Income = 100a Savings = 15a Expenditure = 100a – 15a = 85a According to question New Income = But savings is same Then New Expenditure = 120a – 15a = 105a Required Percentage = Hence, the correct answer is B.
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