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 will from Rs. 3,150 to Rs. 3,250. Taking the original weekly wage of each worker at Rs x ; obtain an equation in x and then solve it to find the weekly wages of each worker.

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Solution

Original weekly wage of each worker = Rs x
Original weekly wage bill of employer = Rs 3150
$N u m b e r space o f space w o r k e r s space equals 3150 over x N e w space w e e k l y space w a g e space o f space e a c h space w o r k e r space equals space x plus 5 N e w space w e e k l y space w a g e space b i l l space o f space e m p l o y e r equals 3250 N u m b e r space o f space w o r k e r equals fraction numerator 3250 over denominator x plus 5 end fraction F r o m space t h e space g i v e n space c o n d i t i o n 3150 over x minus 5 equals fraction numerator 3250 over denominator x plus 5 end fraction 3150 x minus 5 x squared plus 15750 minus 25 x equals 3250 x minus 5 x squared plus 15750 minus 125 x equals 0 x squared plus 25 x minus 3150 equals 0 x squared plus 70 x minus 45 x minus 3150 equals 0 x left parenthesis x plus 70 right parenthesis minus 45 left parenthesis x plus 70 right parenthesis equals 0 left parenthesis x plus 70 right parenthesis left parenthesis x minus 45 right parenthesis equals 0 x equals negative 70 comma 45$

Since, wage cannot be negative, x = 45.
Thus, the original weekly wage of each worker is Rs 45.

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