A boat can go 60 km downstream and 40 km upstream in 12 hours 30 minutes. It can go 84 km downstream and 63 km upstream in 18 hours 54 minutes. What is the speed (in km/h, to the nearest integer) of the boat in still water?

Given:

A boat can go 60 km downstream and 40 km upstream in 12 hours 30 minutes.

It can go 84 km downstream and 63 km upstream in 18 hours 54 minutes.

Concept used:

Upstream speed = Boat speed - speed of the current 

Downstream speed = Boat speed + speed of the current

Distance = speed × time

Calculation:

Downstream speed = x km/h

The upstream speed=  y km/h

As per the question,

60 /x + 40/y = 25/2 ...... (1)

Again, 84/x + 63/y = 189/10 ....... (2)

By solving 1 and 2 we get,

x = 40 / 3 and y = 5

So Still water boat's speed is

⇒ (13..33 + 5) / 2 = 9km/hr

∴ The correct option is 3

Alternate Method 

Let the speed of the boat = u

and

speed of current/river = v

So,

upstream speed (US) = u - v

downstream speed (DS) = u + v

according to the question,

60/DS  +  40/US  = 12.5

⇒ 3/DS + 2/US = 0.625 ....(1)

and

84/(u + v)  + 63/(u - v) = 18.9

⇒ 4/DS + 3/US = 0.9 ....(2)

let 

a = 1/DS   and  b = 1/US

then eq(1) and eq(2) will be

⇒ 3a + 2b  = 0.625 ....(3)

⇒ 4a  + 3b = 0.9....(4)

So, multiply eq(3) with 3 and eq(4) with 2:-

⇒ 9a + 6b = 1.875  ...(5)

⇒ 8a + 6b = 1.8 ....(6)

now,  eq(5) - eq(6)

a = 0.075

then DS = 40/3

and from eq(6)

6b = 1.2

⇒ b = 0.2

⇒ US = 5

Boat speed = (DS + US)/2 = 55/6

Hence; u ≈ 9 km/hr