Question

Three pipes A, B, C are attached to a tank respectively. Pipe A, B are filling pipes that can fill the tank in 45 and 54 minutes while C can empty the tank in 72 Minutes. Pipe A, C are opened for 30 minutes then they are closed, Pipe B and C are opened for 24 minutes then they are closed. After that, all three pipes were opened for the whole time. Find the time taken by all pipes to fill the remaining tank?

1. 680/29
2. 700/31
3. 690/29
4. 690/31

Answer 1

Correct Answer - Option 3 : 690/29

Given:

Pipe A, B are filling pipes that can fill the tank in 45 and 54 minutes.

C can empty the tank in 72 Minutes.

A, C are kept open for 30 minutes, then pipe B and C are opened for 24 minutes.

Calculation:

Let us take the LCM of the time of the three pipes i.e.

LCM of (45, 54, 72) minutes = 1080 units.      ----(1)

Let 1080 units be the capacity of the tank.

⇒ Efficiency of A = (1080/45) = 24 units

⇒ Efficiency of B = (1080/54) = 20 units

⇒ Efficiency of C = (1080/72) = -15 units

(∵ A, B are filling pipes so their efficiency is positive and as C is an empty pipe, its efficiency is negative)

Work was done By A, C in 30 minutes = (24 - 15) × 30 = 270 unit      ----(2)

Now, B, C was opened for 24 minutes,

So, work done by B, C in 24 minutes = (20 - 15) × 24 = 120 units      ----(3)

From (1), (2), (3) we get the left work = 1080 - 270 - 120 = 690 unit

Time taken by all three pipes to fill the Remaining tank (690)/(24 + 20 – 15) = 690/29 min.

∴ The time taken by all pipes to fill the remaining tank is 690/29 min.