Two taps P and Q can fill a tank in 24 hours and 18 hours respectively. If the two taps are opened at 11 a.m., then at what time (in p.m.) should the tap P be closed to completely fill the tank at exactly 2 a.m.?

Let the total capacity of the tank = L.C.M. (24,18) = 72 litres

Tap P fill it in 24 hours, => P's efficiency = $$\frac{72}{24}=3$$ l/hr

Similarly, Q's efficiency = $$\frac{72}{18}=4$$ l/hr

Both taps are opened at 11 a.m., let P be closed after $$'t'$$ hours

=> Q alone operated for = $$(15-t)$$ hours

According to ques, => $$(3+4)t+4(15-t)=72$$

=> $$7t+60-4t=72$$

=> $$3t=72-60=12$$

=> $$t=\frac{12}{3}=4$$

$$\therefore$$ Tap P should be closed after 4 hours = 11 a.m. + 4 hours = 3 p.m.

=> Ans - (C)