#### Question

An employer finds that if he increased the weekly wages of each worker by Rs 5 and employs five workers less, he increases his weekly wage bill from Rs 3,150 to Rs 3,250. Taking the original weekly wage of each worker as Rs x; obtain an equation in x and then solve it to find the weekly wages of each worker.

#### Solution

The original weekly wage of each worker = Rs x

The original weekly wage bill of employer = Rs 3150

Number of workers = 3150/x

New weekly wages of each worker = Rs (x + 5)

The new weekly wage bill of employer = Rs 3250

Number of workers = `3250/(x + 5)`

From the given condition

`3150/x - 5 = 3250/(x + 5)`

`(3150 - 5x)/x = 3250/(x + 5)`

`3150x - 5x^2 + 15750 - 25x = 3250x`

`-5x^2 + 15750 - 125x = 0`

`x^2 + 70x - 45x - 3150 = 0`

x(x + 70) - 45(x + 70) = 0

(x + 70)(x - 45) = 0

x = -70, 45

Since wage cannot be negative x = 45

Thus the original weekly wage of each worker is Rs 45