Boats and Streams
11 solved SSC CGL Quantitative Aptitude previous year questions on Boats and Streams, each with the correct answer and a full explanation.
Q1
A boat can go 5 km upstream and 7 km downstream in 45 minutes. It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km downstream?
✓ Correct answer: b) 12
ExplanationA boat can go 5 km upstream and downstream in 45 minutes.It can also go 5 km downstream and 2.5 km upstream in 25 minutes.Speed of boat during downstream = D km/hr Speed of boat during upstream = U km/hr According to the question, …………..(1) …………..(2) Multiply by 2 both sides ………….(3) Subtract (1) from (3) Speed of boat during downstream = 30 km/hr Time required to go 6 km downstream = Hence, Option B is the correct answer.
Q2
A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him to row three-fifth of the same distance in still water?
✓ Correct answer: b) 7.2
ExplanationLet the distance be D km.Upstream speed = D/18 Downstream speed = D/9 Speed in still water = Hence, the correct answer is (B).
Q3
A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then how much time will it take to go 39 km downstream and 30 km upstream?
✓ Correct answer: b) 3 h 10 m
ExplanationLet the speed of stream be y km/hr Speed of motorboat in still water = 20 km/hr Speed of boat in downstream = (20 + y) km/h Speed of boat in upstream = (20 - y) km/h According to the question, 96y = 400 – y2 y2 + 96y – 400 = 0 y2 + 100y - 4y – 400 = 0 y(y + 100) – 4(y + 100) = 0 (y- 4) (y + 100) = 0 y = 4 km/h Speed of stream is 4 km/h If the speed of boat in still water is increased by 2 km/h, then speed of boat in still water = 20 + 2 = 22 km/h Speed of boat in downstream = 22 + 4 = 26 km/h Speed of boat in upstream = 22 – 4 = 18 km/h Therefore, required time to go 39 km downstream and 30 km upstream = = = = = 3 hour = 3 hour 10 min Hence, the correct answer is (B).
Q4
A boat can cover a distance of 56 km downstream in 3.5 hours. The ratio of the speed of the boat in still water and the speed of the stream is 3 : 1 . How much time (in hours) will the boat take to cover a distance of 41.6 km downstream?
✓ Correct answer: c) 2.6
ExplanationBoat can cover a distance of 56 km downstream in 3.5 hours.Boat can cover a distance of 1 km downstream in hours Boat can cover a distance of 41.6 km downstream in hours Hence, the correct answer is (C).
Q5
A boat moves 25km upstream and 39km downstream in 8 hours. It travels 35km upstream and 52km downstream in 11 hours. What is the speed of the stream if it travels at a uniform speed?
✓ Correct answer: a) 4 km/h
ExplanationLet, the speed of the boat in upstream be x km/h and the speed of downstream be y km/h.According to the question, Multiplying the first equation by 11 and the second equation by 8, we get: Subtracting the second equation from the first equation, we get: Hence, the speed of the boat in upstream be 5 km/h and the speed of downstream be 13 km/h.Let, the speed of the boat in still water be p km/h and the speed of the stream be q km/h. p-q=5 ... iii p+q=13 ...iv Subtracting the fourth equation from the third equation, we get: q=4 Therefore, the speed of the stream is 4 km/h.Hence, the correct answer is (A).
Q6
A boat covers a certain distance against the stream in 9 hours 36 min and it covers the same distance along the stream in 6 hours. What is the ratio of the speed of the boat in still water to that of the stream?
✓ Correct answer: a) 13:3
ExplanationLet's denote the speed of the boat in still water as km/h and the speed of the stream as km/h.Speed against the stream = km/h Speed along the stream = km/h Against the stream: 9 hours 36 minutes = hours Along the stream: 6 hours Distance against the stream = Distance along the stream So, the ratio of the speed of the boat in still water to that of the stream is 13:3. Option A: 13:3 is the correct answer.
Q7
A boat can cover upstream and back in a total of 30 hours, and upstream and downstream in a total of 7 hours. How much distance will the boat cover in 16 hours in still water?
✓ Correct answer: a) 200 km
ExplanationLet, speed of boat is km/h and speed of stream is km/h Then, according to question and, From equation (1) and (2), Hence, Boat can cover distance in still water in 16 hours is = km.Hence, the correct answer is (A).
Q8
A boat running upstream takes 10 hours to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and that of the water current, respectively?
✓ Correct answer: d) 17: 3
ExplanationA boat takes 10 hours to cover a certain distance running upstream, Boat upstream speed (x-y) = km/hr ...(1) where, x= speed of boat , y = speed of stream Boat takes 7 hours to cover the same distance running downstream , Boat downstream speed (x+y) = km/hr ...(2) By solving equations (1) and (2), we get: x = km/hr y = km/hr The ratio between the speed of the boat (x) and that of the water current (y) = 17 : 3 Hence, the correct option is D.
Q9
A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
✓ Correct answer: c) 8 km/h
ExplanationLet, Speed of boat in still water = x km/hr | | SSC Speed of stream = y km/hr Speed of boat in upstream = (x-y)km/hr Speed of boat in downstream = (x+y)km/hr According to the given question, From Therefore, Speed of boat in still water is 8km/hr.Hence, The correct option is (C).
Q10
A boat covers 35 km downstream in 2 h and covers the same distance upstream in 7 h . Find the speed (in km/h) of the boat in still water.
✓ Correct answer: a) 11.25
ExplanationWe know that, Speed = ∴ The downstream speed= km/hr ∴ The upstream speed= km/hr ∴ The speed of the vessel= Hence, Option A is the correct answer.
Q11
To go a distance of 144 km upstream, a rower takes 12 hours while it takes her only 9 hours to row the same distance downstream.What is the speed of the stream?
✓ Correct answer: d) 2 km/h
ExplanationLet, speed of boat be km/hr and speed of stream be km/hr So, according to question and, From equations (1) and (2) = 14 km/hrs and = 2 km/hrs Hence, the correct answer is (D).
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