Question
Download Solution PDFA cistern has an inlet pipe and an outlet pipe. Inlet pipe can fill three-fourth of the cistern in 24 minutes while outlet pipe can empty the one-third filled cistern in 16 minutes. If both the pipes are opened together, then the cistern will be completely filled in-
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Inlet pipe can fill three-fourths of the cistern in 24 minutes.
Outlet pipe can empty one-third of the cistern in 16 minutes.
Calculations:
Rate of the inlet pipe = (3/4) cistern / 24 minutes = 3 / (4 × 24) = 1 / 32 cistern per minute.
Rate of the outlet pipe = (1/3) cistern / 16 minutes = 1 / (3 × 16) = 1 / 48 cistern per minute.
When both pipes are opened together, the combined rate is:
Combined rate = Rate of inlet pipe - Rate of outlet pipe = 1/32 - 1/48
To subtract, find the LCM of 32 and 48, which is 96:
1/32 = 3/96, and 1/48 = 2/96, so combined rate = (3/96) - (2/96) = 1/96 cistern per minute.
Thus, the cistern will be filled in 96 minutes.
∴ The cistern will be completely filled in 96 minutes.
Last updated on Jul 3, 2025
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