Discussion

Explanation:

P, Q and R together can complete the whole work in 6 hours.
∴ In 2 hours they would have completed 2/6 = 1/3^rd of the tank

The remaining 2/3^rd of the tank is filled by P and Q in 7 hours.
If P and Q can fill 2/3^rd tank in 7 hours, they can fill the whole tank in 7 × 3/2 = 10.5 hours.
Combined efficiency of P and Q = $\frac{1}{10.5}$

P, Q and R together can complete the whole work in 6 hours.
⇒ $\frac{1}{6}=\frac{1}{\mathrm{P}}+\frac{1}{\mathrm{Q}}+\frac{1}{\mathrm{R}}$

Now, $\frac{1}{\mathrm{P}}+\frac{1}{\mathrm{Q}}$ is combined efficiency of P and Q which will be $\frac{1}{10.5}$

⇒ $\frac{1}{6}=\frac{1}{10.5}+\frac{1}{\mathrm{R}}$

⇒ $\frac{1}{\mathrm{R}}=\frac{1}{6}-\frac{1}{10.5}$

⇒ R = 42/3 = 14 hours

Hence, option (c). 

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