\( P \) या नळाने एक टाकी भरण्यास 10 तास लागतात, तर \( Q \) या नळाने ती टाकी रिकामी होण्यास 14 तास लागतात. जर दोन्ही नळ एकाच वेळी सुरू केले आणि 7 तासानंतर \( Q \) नळ बंद केला, तर ती टाकी पूर्ण भरण्यास एकूण किती वेळ लागेल?

\( P \) (fills) = 10 hours; \( Q \) (empties) = 14 hours.
\( \text{LCM}(10, 14) = 70 \) (tank capacity).
Efficiency of \( P \) = \( \frac{70}{10} = 7 \) units/hr.
Efficiency of \( Q \) = \( \frac{70}{14} = 5 \) units/hr.

During the first 7 hours (while both \( P \) and \( Q \) are running):
Cumulative efficiency = \( 7 - 5 = 2 \) units/hr.
Tank filled in 7 hours = \( 2 \times 7 = 14 \) units.

Balance tank filling capacity: \( 70 - 14 = 56 \) units.

When the \( Q \) tap is closed: Only the \( P \) tap will remain working.
Efficiency of \( P \) = 7 units/hr.
Time taken to fill the balance tank = \( \frac{56}{7} = 8 \) hrs.

Total time taken to fill full tank: \( 7 \text{ hours} + 8 \text{ hours} = 15 \text{ hours} \).