Question

Pipes X and Y are the filling pipes while Z is an empty pipe. X, Y can fill the given empty tank In 45 and 54 minutes respectively. However, pipe Z can empty in 90 minutes. If all the pipes are opened Together for 10 minutes after that pipe is A and B is blocked and Now, only pipe Z is opened. Find the total time taken by pipe Z to empty the filled tank?

1. 70/3
2. 80/3
3. 73/3
4. 70/4

Answer 1

Correct Answer - Option 2 : 80/3

Given:

X, Y can fill the given empty tank In 45 and 54 minutes respectively.

Pipe Z can empty in 90 minutes.

After 10 minutes X, Y are blocked and only pipe Z is opened.

Concept used:

Efficiency = (Total work)/(Time taken)

Calculation:

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

LCM of (45, 54, 90) minutes = 270 unit.

Let the Capacity of the tank is 270 units.

⇒ Efficiency of X = (270/45) = + 6 units

⇒ Efficiency of Y = (270/54) = + 5 units

⇒ Efficiency of Z = (270/90) = - 3 units

(∵ X, Y are filling pipes so their efficiency is positive and as Z is an empty Pipe its efficiency is negative)

Pipes X, Y, Z are all opened for 10 minutes,

⇒ Work done by all in 10 minutes = (+ 6 + 5 – 3) × 10 = 80 units      -----(1)

∴ Time Taken by Z to Empty 80 units of tank is (80/3) minutes.