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 remining part in 7 hours. The number of hours taken by R alone to fill the tank is:

Let us assume the Capacity of the tank = 42 L i.e. the LCM of 6, 7 and 2.
Combined efficiency of P, Q and R = 42/6 = 7 Litres per hour.
In 2 hours, P, Q and R can fill 7*2 = 14 Litres.
The remaining 42 - 14 = 28 litres was filled by P and Q in 7 hours. This gives the combined efficiency of P and Q = 28/7 = 4 litres per hour.
By subtracting the two equations of efficiency, we get that efficiency of Pipe R = 7 - 4 = 3 Litres per hour.
Time taken by Pipe R alone to fill the tank = 42/3 = 14 hours.