Question
Download Solution PDFTwo pipes C and D can fill a tank in 6 hours and 9 hours, respectively. They are opened alternately for | hour each, starting with C first. In what duration, will the tank be filled?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Pipe C fills tank in 6 hours.
Pipe D fills tank in 9 hours.
Pipes are opened alternately for 1 hour each, starting with C.
Formula used:
LCM method to find total capacity.
Efficiency = Total capacity / Time.
Calculations:
LCM of 6 and 9 = 18 (Total capacity).
Efficiency of C = 18 / 6 = 3 units/hour.
Efficiency of D = 18 / 9 = 2 units/hour.
In 2 hours (C then D), work done = 3 + 2 = 5 units.
In 6 hours (3 cycles of 2 hours), work done = 5 × 3 = 15 units.
Remaining work = 18 - 15 = 3 units.
Next hour, C works and fills 3 units.
Total time = 6 + 1 = 7 hours.
∴ The tank will be filled in 7 hours.
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