Question 1

A pipe can empty a full cistern in 8 hours. If the cistern is already 3/4 full, how long will it take for the pipe to empty it completely?

Accepted Answer

Step 1: The pipe empties the entire cistern in 8 hours, so its rate = 1/8 cistern per hour. Step 2: The cistern is 3/4 full, so we need to empty 3/4 of the cistern. Step 3: Time required = (3/4) ÷ (1/8) = (3/4) × 8 = 6 hours. Therefore, the answer is 6 hours.

Question 2

A pipe can empty a full cistern in 20 hours. If the cistern is already 3/4 full, how long will it take to empty it completely?

Accepted Answer

Step 1: The pipe empties the entire cistern in 20 hours. Step 2: To empty 3/4 of the cistern, time required = (3/4) × 20 = 15 hours. Therefore, answer is 15 hours.

Question 3

Pipe A can fill a cistern in 12 hours, and Pipe B can empty it in 18 hours. If both pipes are opened simultaneously, how long will it take to fill the cistern?

Accepted Answer

Step 1: Rate of Pipe A = 1/12 per hour (filling). Step 2: Rate of Pipe B = 1/18 per hour (emptying). Step 3: Net rate = 1/12 - 1/18 = (3-2)/36 = 1/36 per hour. Step 4: Time to fill = 1 ÷ (1/36) = 36 hours.

Question 4

Pipe A can fill a cistern in 12 hours, and Pipe B can empty it in 18 hours. If both pipes are opened simultaneously, how long will it take to fill the cistern?

Accepted Answer

Step 1: Rate of Pipe A (filling) = 1/12 per hour. Step 2: Rate of Pipe B (emptying) = 1/18 per hour. Step 3: Net rate = 1/12 - 1/18 = (3-2)/36 = 1/36 per hour. Step 4: Time to fill = 1 ÷ (1/36) = 36 hours.

Question 5

Two pipes A and B together can fill a tank in 10 hours. If Pipe A alone takes 6 hours more than Pipe B alone to fill the tank, how long will Pipe B take to fill the tank individually?

Accepted Answer

Step 1: Let B take x hours, then A takes (x+6) hours. Step 2: Rate of A = 1/(x+6), Rate of B = 1/x. Step 3: Combined rate = 1/(x+6) + 1/x = 1/10. Step 4: Multiply through by 10x(x+6): 10x + 10(x+6) = x(x+6). Step 5: 10x + 10x + 60 = x² + 6x. Step 6: 20x + 60 = x² + 6x. Step 7: x² - 14x - 60 = 0. Step 8: Using quadratic formula or factoring: (x-20)(x+3) = 0. Step 9: x = 20 (taking positive value). Therefore, Pipe B takes 20 hours.

Agniveer Army GD Pipes & Cisterns

Pipes & Cisterns — Practice Questions