Question

An employer finds that if he increases 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.

Answer 1

Original weekly wage of each worker = Rs. x

Original weekly wage bill of employer = Rs. 3150

Number of workers = `3150/x`

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

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 – 5x² + 15750 – 25x = 3250x

–5x² + 15750 – 125x = 0

x² + 25x – 3150 = 0

x² + 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