Question:
Two pipes 'A' and 'B' can fill a water tank in 30 minutes and 20 minutes, respectively. Initially pipe 'A' was opened and after 5 minutes, pipe 'B' was also opened. Find the total time (in minutes) taken by the pipes to fill the tank.
Two pipes 'A' and 'B' can fill a water tank in 30 minutes and 20 minutes, respectively. Initially pipe 'A' was opened and after 5 minutes, pipe 'B' was also opened. Find the total time (in minutes) taken by the pipes to fill the tank.
Updated On: Sep 16, 2026
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- 15
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The Correct Option is D
Solution and Explanation
Concept:
Step 1: Find the rate of each pipe
Pipe A fills the tank in 30 minutes, rate of A = 1/30 per minute
Pipe B fills the tank in 20 minutes, rate of B = 1/20 per minute
Step 2: Find the work done by A alone in the first 5 minutes
Work done = 5 x (1/30) = 5/30 = 1/6 of the tank
Remaining work = 1 - 1/6 = 5/6 of the tank
Step 3: Find the combined rate once B joins, and the time to finish the remaining work
Combined rate = 1/30 + 1/20 = 2/60 + 3/60 = 5/60 = 1/12 per minute
Time for remaining 5/6 = (5/6) ÷ (1/12) = (5/6) x 12 = 10 minutes
Step 4: Find the total time taken
Total time = 5 minutes (A alone) + 10 minutes (both together) = 15 minutes
Final Answer: 15 minutes
- Work done by a pipe in 1 minute = 1/(time taken to fill the tank alone).
- When one pipe works alone first, subtract the work already done from the total before the second pipe joins.
- Once both pipes work together, add their individual rates to get the combined rate.
Step 1: Find the rate of each pipe
Pipe A fills the tank in 30 minutes, rate of A = 1/30 per minute
Pipe B fills the tank in 20 minutes, rate of B = 1/20 per minute
Step 2: Find the work done by A alone in the first 5 minutes
Work done = 5 x (1/30) = 5/30 = 1/6 of the tank
Remaining work = 1 - 1/6 = 5/6 of the tank
Step 3: Find the combined rate once B joins, and the time to finish the remaining work
Combined rate = 1/30 + 1/20 = 2/60 + 3/60 = 5/60 = 1/12 per minute
Time for remaining 5/6 = (5/6) ÷ (1/12) = (5/6) x 12 = 10 minutes
Step 4: Find the total time taken
Total time = 5 minutes (A alone) + 10 minutes (both together) = 15 minutes
Final Answer: 15 minutes
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