Question

A pipe can fill a tank in x hours and another can empty it in y hours . If the tank is 1/3rd full then the number of hours in which they will together fill it in is.

Answer 1

(1/X + 1/Y)t=2/3
t= (2(X+Y))/3Y

Answer 2

ANSWER:  

Time taken to complete 2/3rd of tank is  $\frac{2 x y}{3(y-x)} \text {hours}$

SOLUTION:

Given, a pipe can fill tank in x hours, then work done in one hour = $\frac{1}{x}$

Another pipe can empty tank in y hours, then work done in one hour = $\frac{1}{y}$

Then, together work done in 1 hour = $\frac{1}{x}-\frac{1}{y}=\frac{y-x}{x y}$

Now, time taken to complete work together is $\frac{x y}{y-x}$

As 1/3rd of tank is already filled, we need to fill 2/3rd of the tank.

Now time taken to fill 2/3rd of tank  $=\frac{2}{3} \frac{x y}{y-x}=\frac{2 x y}{3(y-x)}$

Hence the time taken to complete 2/3rd of tank is  $\frac{2 x y}{3(y-x)} \text {hours}$