Question

In a cold drink factory, a tank in which cold drink is poured can be completely fill through 3 pipes A, B and C in 120, 60 and 30 minutes. A worker open pipes B and C for 10 minutes and then close pipe B while pipe A remained opened. Then he closed the pipe C 10 minutes before the cold drink overflows from the tank. How long does if take to fill the tank?
1. 30 minutes
2. 40 minutes
3. 28 minutes
4. 36 minutes

Answer 1

Correct Answer - Option 1 : 30 minutes

Given∶

 Time required to fill the tank by pipes A, B and C = 120, 60 and 30 minutes.

Pipe C is closed 10 min. before the tank over flows.  

Formula Used∶

An inlet can fill a tank in X min. and another inlet in Y min. If both the inlets are opened at the same time, the net part of the tank filled in one minute is

given by ; (1/x + 1/y)

Calculation∶

In one minute, pipe A fills (1/120) of the tank, pipe B fills (1/60) of the tank and pipe C fills (1/30) of the tank.

Pipes (B + C) opened for 10 minutes, followed by pipes (A + C) opened for 't' minutes, followed by pipe A which opened for 10 minutes. This ensures that the tank gets filled. This can be written in equation form:

(1/60 + 1/30) × 10 + (1/120 + 1/30) × t + (1/120) 10 = 1

⇒ 10 × (3/60) + t × (1/24) + 10 × (1/120) = 1

⇒ 1/2 + t/24 + 1/12 = 1

⇒ t = 24 - 14 = 10

So, the entire tank was filled in 30 minutes.

∴ It takes 30 minutes to fill the tank.