P and Q together can fill a cistern with water in 12 hours. If P alone can fill the cistern with water in 14 hours, then in how many hours will Q alone fill one-fourth of the same cistern with water? P और Q मिलकर एक टंकी को 12 घंटे में पानी से भर सकते हैं। यदि P अकेले उसी टंकी को 14 घंटे पानी से भर सकता है, तो Q अकेले टंकी का एक-चौथाई भाग कितने घंटे में भरेगा?

P and Q together can fill a cistern with water in 12 hour... - Time and Work MCQ Solution

P and Q together fill the cistern in 12 hours
Combined rate = $\frac{1}{12}$ tank per hour

P alone fills in 14 hours
⇒ Rate of P = $\frac{1}{14}$ tank per hour

Rate of Q = Combined rate − Rate of P

$= \frac{1}{12} - \frac{1}{14}$

LCM of 12 and 14 = 84

$= \frac{7 - 6}{84} = \frac{1}{84}$

So, Q alone fills the whole tank in 84 hours.

Time = $84 \times \frac{1}{4} = 21$ hours

Correct Answer: 21 hours