Three pipes P, Q and R can fill a tank in 12 hours. After working at it together for 4 hours, R is closed. P and Q can fill the remaining tank in 14 hours. What is the number of hours taken by R alone to fill the tank?

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Solution

The correct option is C
28

Part filled in 4 hours = $\frac{4}{12}$ = $\frac{1}{3}$

Remaining part = 1 - $\frac{1}{3}$ = $\frac{2}{3}$

(P + Q)'s 1 hour work = $\frac{2}{3} \times \frac{1}{14}$ = $\frac{1}{21}$

R's 1 hour work = [(P + Q + R)'s 1 hour work - (P + Q)'s 1 hour work] = ( $\frac{1}{12}$ - $\frac{1}{21}$ ) = $\frac{1}{28}$

R alone can fill the tank in 28 hours.

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Three pipes P, Q and R can fill a tank in 12 hours. After working at it together for 4 hours, R is closed. P and Q can fill the remaining tank in 14 hours. What is the number of hours taken by R alone to fill the tank?

The correct option is C 28 Part filled in 4 hours = 412 = 13 Remaining part = 1 - 13 =23 (P + Q)'s 1 hour work = 23×114 =121 R's 1 hour work = [(P + Q + R)'s 1 hour work - (P + Q)'s 1 hour work] = (112 - 121) =128 R alone can fill the tank in 28 hours.