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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.
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Solution
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
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