A motorboat traveling at some speed can cover 24 km upstream and 40 km downstream in 17 hours. At the same speed, it can travel 32 km downstream and 12 km upstream in 10 hours. The speed of the stream is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 3 km/h.
Let the speed of baat be x and the speed of the stream be y
Speed upstream = x − y
Speed downstream = x + y
We know that,
Time = Distance/Speed
For the first scenario:
⇒ 24/(x - y) + 40/(x + y) = 17.....(1)
For the second scenario:
⇒ 12/(x - y) + 32/(x + y) = 10.....(2)
Now, let 1/(x - y) = u and 1/(x + y) = v
⇒ 24u + 40v = 17.....(3)
⇒ 12u + 32v = 10.....(4)
Multiplying eq 2 by 2 and subtracting eq 1 from eq 2
⇒ 24u + 64v - 24u - 40v = 20 - 17
⇒ 24v = 3
⇒ v = 1/8 and
Similarly, u = 1/2
⇒ 1/(x - y) = u
⇒ 1/(x - y) = 1/2
⇒ x - y = 2.....(5)
⇒ 1/(x + y) = v
⇒ 1/(x + y) = 1/8
⇒ x + y = 8.....(6)
Solving equation 5 and 6
⇒ 2x = 10
⇒ x = 5
and y = 3
Thus, The speed of the stream is 3 km/hr