Question

A person can row a boat 32 km upstream and 72 km downstream in 10 hours. Also, he can row 48 km upstream and 84 km downstream in 13 hours. Find the rate of the current. 
1. 2 km per hr
2. 4 km per hr.
3. 6 km per hr.
4. 8 km per hr.

Answer 1

Correct Answer - Option 1 : 2 km per hr

Given 

A person can row a boat 32 km upstream and 72 km downstream in 10 hours.

He can row 48 km upstream and 84 km downstream in 13 hours

Let the upstream speed be x km per hr. and downstream speed by y km per hr.

Then, we can write

32/x + 72/y = 10

And, 48/x + 84/y = 13

Let 1/x = m and 1/y= n

The above two equations can now be written as

Calculation
32 m + 72 n = 10     ...(i)

and, 48 m + 84 n = 13     ...(ii)

3 × (i) – 2 × (ii) gives 48n = 4 

⇒ n = 1/12

So, y = 12 km/h

Put the value of n in equation (i)

 32 m + 6 = 10

Then m = 4/32 = 1/8

So, x = 8 km/h

Rate of current

=(y - x) / 2

=(12 - 8) / 2

= 2 km per hr