Question

An employer finds that if he increases the weekly wages of each worker by five and employer five worker less he increases his weekly wages bill from 3150 to 3250. Taking the original weekly wage of each work er as ₹x obtain an equation in and then solve it to find weekly wages of each work​​

Answer 1

let number of employee initially be n

wage of one employee = x

weekly wages = nx = 3150

n = 3150/x

now

new wage per employee = x + 5

no. of employee = (n - 5)

weekly wages = 3250

(n-5)(x+5) = 3250

nx + 5n - 5x - 25 = 3250

3150 + 5n - 5x - 25 = 3250

5n - 5x = 3250 - 3150 + 25

5n - 5x = 125

n - x = 25

3150/x - x = 25

3150 - x^2 = 25x

x^2 + 25x - 3150 = 0

3150 = 5 x 3 x 7 x 2 x 5 x 3

= 5*3*3 x 5*2*7

= 45*70 (70-45 = 25)

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

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

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

x = 45, -70

wage cannot be negative

hence, x = 45