Pipes A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then the times in which A and will fill the cistern separately will be respectively

Let time taken by A alone to fill the cistern = $$t$$ minutes

=> Time taken by B = $$(t+5)$$ minutes

According to ques, => $$\frac{1}{t}+\frac{1}{t+5}=\frac{1}{6}$$

=> $$\frac{t+t+5}{t(t+5)}=\frac{1}{6}$$

=> $$12t+30=t^2+5t$$

=> $$t^2-7t-30=0$$

=> $$(t-10)(t+3)=0$$

=> $$t=10,-3$$

$$\because$$ Time cannot be negative, => $$t=10$$

Thus, time taken by A and B separately to fill the cistern is 10 min and 15 min respectively.

=> Ans - (C)