A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If both pumps are used together, how long will the tank take to fill?

Question

Bright Tutorials · Accepted Answer

Let x litres be the capacity of the tank.
Then, water filled by small tank in one hour = $\frac {x}{3}$ litre
Water filled by large tank in one hour = $\frac {x}{2}$ litre
So, total water filled by both pumps in one hour = $\left(\frac{x}{3}+\frac{x}{2}\right)$ litre = $\frac {5x}{6}$ litre
∴ Time taken by both pumps used together to fill the tank = $\left(1 \div \frac{5 x}{6}\right) \times x$
= 1 × $\frac {6}{5x}$ × x
= $\frac {6}{5}$ hour
= 1$\frac {1}{5}$ hour

Proportional Reasoning 2 — Question 10