Question

A tank can be filled by two taps X and Y in 5 hrs and 10 hrs respectively while another tap Z empties the tank in 20 hrs. In how many hours can the tank be filled, if all 3 taps are kept open?

• A. 5
• B. 4
• C. 7
• D. 8

Answer 1

Answer:

B. 4

The efficiency of X = $\frac{1}{5}$

The efficiency of Y = $\frac{1}{10}$

The efficiency of Z = $\frac{1}{[20}$

⇒ Total efficiency of X, Y and Z = $(\frac{1}{5}) + (\frac{1}{10})-(\frac{1}{20})=\frac{1}{4}$

∴ The total time taken is 4 hours

Shortcut Trick

When all taps are opened, then efficiency is

⇒ 4 + 2 - 1 = 5

The capacity of tank = 20

Time is taken to fill the tank 

⇒ $\frac{20}{5}$

⇒ 4

∴ The total time taken is 4 hours.