Two pipes A and B can fill a water tank in 20 minutes and 24 minutes r

1.	Two pipes A and B can fill a water tank in 20 minutes and 24 minutes respectively and the third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together fill the tank in 15 minutes, the capacity (in gallons) of the tank is (a) 180 (b) 150 (c) 120 (d) 60
Answer» Part of the tank filled when all the three pipes are opened in 1 minute = \(\frac{1}{15}\) Part of the tank filled when (A + B) are opened in 1 minute = \(\frac{1}{20}\)+\(\frac{1}{24}\)= \(\frac{6+5}{120}\) = \(\frac{11}{120}\) \(\therefore\) Part of the tank emptied by C in 1 min. = \(\frac{11}{120}\) - \(\frac{1}{15}\) = \(\frac{1}{40}\) \(\therefore\) Capacity of \(\frac{1}{40}\) part of the tank = 3 gallons \(\therefore\) Capacity of the tank = (3 × 40) gallons = 120 gallons.

Two pipes A and B can fill a water tank in 20 minutes and 24 minutes respectively and the third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together fill the tank in 15 minutes, the capacity (in gallons) of the tank is (a) 180 (b) 150 (c) 120 (d) 60

Answer»

Part of the tank filled when all the three pipes are opened in 1 minute = \(\frac{1}{15}\)

Part of the tank filled when (A + B) are opened in 1 minute = \(\frac{1}{20}\)+\(\frac{1}{24}\)= \(\frac{6+5}{120}\) = \(\frac{11}{120}\)

\(\therefore\) Part of the tank emptied by C in 1 min. = \(\frac{11}{120}\) - \(\frac{1}{15}\) = \(\frac{1}{40}\)

\(\therefore\) Capacity of \(\frac{1}{40}\) part of the tank = 3 gallons

\(\therefore\) Capacity of the tank = (3 × 40) gallons = 120 gallons.