Taps P, Q, and R can fill a tank in 20, 25, and 40 hours respectively. Taps Q is kept open for 10 hours, and then tap Q is closed, after that tap P and R are opened. Tap R is closed 9 hours before the tank overflows. How long does it take to fill the tank?

Question

Question

Answer 1

Given:

Tap P can fill a tank = 20 hours

Tap Q can fill a tank = 25 hours

Tap R can fill a tank = 40 hours

Calculation:

Let the total work be LCM of 20, 25, and 40 = 200 units

⇒ Efficiency of tap P = 200/20 = 10 units

⇒ Efficiency of tap Q = 200/25 = 8 units

⇒ Efficiency of tap R = 200/40 = 5 units

Since the tap Q is kept open for 10 hours,

Work done by tap Q = 10 × 8 = 80 units

∵ Tap R is closed 9 hours before the tank overflows

⇒ Tap P alone worked for 9 hours.

⇒ Work done by tap P alone = 9 × 10 = 90 units

Remaining work = 200 - (80 + 90) = 30 units

The remaining work was done by tap P and tap R together

Time taken by tap P and Tap R to complete the remaining work = 30/(10 + 5) = 30/15 = 2 hours

∴ The total time to fill the tank is (10 + 9 + 2) 21 hours.