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 both P and Q can fill the remaining part in 7 hours. The number of hours that will be taken by R alone to fill the tank is

It is given that P, Q and R together can complete the work in 6 hrs.

P, Q and R together worked for 2 hours, this implies they completed 1/3rd of the work.

R left and remaining work is finished by P and Q in 7 hours.

Therefore, P and Q completed 2/3rd of the work in 7 hours.

This implies P and Q together can complete the work in 21/2 hours.

Let the total work be LCM(6, 21/2), i.e. 42 units.

P, Q and R together can complete 7 units in one hour.

P and Q together can complete 4 units in one hour.

This implies, R can complete 3 units in one hour.

Time taken by R alone to complete the work = $$\frac{42}{3}$$ = 14 hours

The answer is option C.