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?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 2)

Answer 1

Given:

A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream.

Concept used:

1. Distance = Speed × Time

2. While rowing upstream, the upstream speed is the difference between the speed of the boat in still water and the speed of the flow.

3. While rowing downstream, the downstream speed is the addition of the speed of the boat in still water and the speed of the flow.

4. Componendo-Dividendo Method

Calculation:

Let the distance, speed of the boat in still water, and speed of the river be D, S, and R respectively.

According to the concept,

D/(S - R) = 18 ....(1)

D/(S + R) = 9 ....(2)

(1) ÷ (2),

(S + R)/(S - R) = 2

⇒ \(\frac {S + R + S - R}{S + R - S + R} = \frac {2 + 1} {2 - 1}\) (Componendo-Dividendo Method)

⇒ \(\frac {S}{R} = 3\)

⇒ S = 3R

Putting S = 3R in (1), D = 36R

Now, time taken to row three-fifth of the same distance in still water = \(36R \times \frac {3}{5} \div 3R\) = 7.2 hours

∴ It will take 7.2 hours to row three-fifth of the same distance in still water.

Shortcut Trick

Let's assume the total distance be 180 km

So, down-stream speed will be 180/9 = 20 km/hr

So, up-stream speed will be 180/18 = 10 km/hr

Now, speed of the boat will be (20 + 10)/2 = 15 km/hr

So,the boat can row (3/5^th of 180km) 108 km in 108/15 = 7.2 hr