Question

Rakesh and Siddharth row on a river simultaneously from the same point. Rakesh rows downstream and Siddharth rows upstream. In 15 min, they are 2.25 km apart. Rakesh then turns to follow Siddharth and after 30 min from the beginning, the boats have rowed together 3.5 km. If the speeds of Rakesh and Siddharth and the stream are constant at how many km/hour does the stream flow?

• A. 3 km
• B. 2.5 km
• C. 2 km
• D. 5 km

Answer 1

The correct option is C 2 km

Let the speed of Siddharth and Rakesh be x an y km/h, respectively,
And the speed of stream = $akm/h$
Case I:
As Rakesh rows downstream and Siddharth rows upstream:
That is, $(x-a)\times \frac{15}{60}+(y+a)\frac{15}{50}=2.25x-a+y+a=9\left(i\right)x+y=9$
Case II:
$(x-a)\times \frac{15}{60}+(y-a)\frac{15}{60}=1.25x-a+y-a=5(x+y-2a=5)\left(ii\right)$
On solving (i) and (ii)
We get a = 2 km/h