Question

1. A swimming pool can be filled in 4 hours by 8 pumps of the same type. How
many such pumps are required if the pool is to be filled in 11/4 hours?
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Answer 1

Unitary method :

In 4 hours  = 8 pumps can fill the swimming pool

In 1 hour = 8/4

In 11/4 (2.75) hours = 8/4 * 11/4 = 88/16 = 5.5 pumps

Proportion method :

Let the required pumps to fill the swimming pool be x

Proportion :  4 : 2.75 : : 8 : x

We know that, Product of means = Product of extremes

Here extremes = 4, x  ; means =2.75, 8

$\tt{2.75 \times 8 = 4 \times x}$

$\tt{22 = 4x}$

$\tt{\frac{22}{4} = x}$

$\tt{x = \frac{11}{2}}$

$\tt{x = 5.5}$

Therefore 5.5 pumps are required if the pool is to be filled in 11/4 hours.