Two pipes, A and B, can fill a tank of 3700 litres in 9 hours and 6 hours, respectively. If they are opened together, how many hours will they take to fill an empty tank of 6400 litres?​

Correct option is A

Given:

Pipe A fills 3700 L in 9 h

rate $$r_A=\dfrac{3700}{9}$$​ L/h

Pipe B fills 3700 L in 6 h

rate $$r_B=\dfrac{3700}{6}$$​ L/h

Target tank capacity = 6400 L

Formula Used:

Time $$=\dfrac{\text{Volume}}{\text{Rate}}$$​​

Solution:
Combined rate:
​$$r_A+r_B=\frac{3700}{9}+\frac{3700}{6}$$​​
​$$=3700\left(\frac{1}{9}+\frac{1}{6}\right)$$​​

​$$=3700\left(\frac{5}{18}\right)=\frac{18500}{18}\ \text{L/h}$$​​
Time to fill 6400 L:
t$$=\frac{6400}{\frac{18500}{18}}=\frac{6400\times 18}{18500}$$​​

=$$\frac{1152}{185}$$hours