Three pipes P, Q and R can fill a tank in 6 hours. After working at it together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the tank is:
Explanation:
P, Q and R together can complete the whole work in 6 hours. ∴ In 2 hours they would have completed 2/6 = 1/3rd of the tank
The remaining 2/3rd of the tank is filled by P and Q in 7 hours. If P and Q can fill 2/3rd tank in 7 hours, they can fill the whole tank in 7 × 3/2 = 10.5 hours. Combined efficiency of P and Q = 110.5
P, Q and R together can complete the whole work in 6 hours. ⇒ 16=1P+1Q+1R
Now, 1P+1Q is combined efficiency of P and Q which will be 110.5
⇒ 16=110.5+1R
⇒ 1R=16-110.5
⇒ R = 42/3 = 14 hours
Hence, option (c).
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