Question

Three filling pipes can fill a tank in 34, 68 and 51 minutes respectively. An emptying pipe can empty the same tank in 17 minutes. Find the total time taken by the pipe to fill it when all the pipes are opened simultaneously.
1. 200
2. 208
3. 204
4. 210

Answer 1

Correct Answer - Option 3 : 204

Given: Three filling pipes can fill a tank in 34, 68 and 51 minutes respectively. An emptying pipe can empty the same tank in 17 minutes.

Formula: If the time taken by pipes P1, P2,..Pn to fill a tank is p1, p2, ...pn and the time taken by pipes Q1, Q2, ..., Qn to empty it be q1, q2,..., qn respectively and the total time taken by all the pipes to fill the tank is t.

1/t = (1/p1 + 1/p2 + ... + 1/pn) – (1/q1 + 1/q2 + ... + 1/qn)

Efficiency is inversely proportional to time taken for doing work.

Total work = Efficiency × time

Calculation:

LCM of 34, 68, 51 and 17 is 204

Let the total work = 204 units

Efficiency of 1^st pipe or 1 minute work = 204/34 = 6

Efficiency of 2^nd pipe or 1 minute work = 204/68 = 3

Efficiency of 3^rd pipe or 1 minute work = 204/51 = 4

Efficiency of 4^th pipe or 1 minute work = 204/17 = -12 (emptying pipe)

Effective rate of capacity of all 4 pipes or 1 min. work by all pipe together = 6 + 3 + 4 – 12 = 1 unit

Total time taken to fill the tank = 204/1 = 204 minutes.