Question 2

Two boats P and Q run between two cities A and B on a stream with flow of 5 km/h. The cities are 300 km apart and P and Q have still water speeds of 25 km/h and 15 km/h respectively. P and Q start from cities A and B towards B and A respectively at the same time. When and where will they meet for the second time?

Solution

Effective speed of boat P (starting from city A) = 25+5 = 30 km/hr  (downstream)

Effective speed of boat Q (starting from city B) = 15-5 = 10 km/hr  (upstream)

Boat P is faster. i.e. P reaches city B in $$ \frac{300}{30} $$ = 10 hrs.

In 10 hrs, Q travels 10 x 10 = 100 km (from city B)

After 10hrs, P travels upstream. Effective speed of P = 25 - 5 = 20 km/hr

Effective speed of Q = 10 km/hr

Let the boats meet after time t and at a distance s from city B

Distance to be travelled by P = s

Distance to be travelled by Q = s - 100

Equating time taken by P and Q, 

$$ \frac{s}{20} =  \frac{s-100}{10} $$

2(s - 100) = s 

i.e. s = 200 km

t = 10 + $$ \frac{200}{20} $$ = 20hrs

The boats will meet 2nd time after 20hrs, 200km from city B.

Therefore, Option D is correct.

 


Create a FREE account and get:

  • Download RRB Study Material PDF
  • 45+ RRB previous papers with solutions PDF
  • 300+ Online RRB Tests for Free

cracku

Boost your Prep!

Download App