Question
The director of a start-up with 8 full-time employees
decided to distribute a portion of the annual profit as bonuses to the employees. However, it was later discovered that, in addition to the full-time employees, some freelancers were also included in the profit distribution. As a result, the bonus each employee received decreased by Rs. 150. To address this, the director increased the total bonus amount by Rs. 1320, ensuring that each employee now receives Rs. 520 as a bonus. What was the original bonus amount each full-time employee was supposed to receive initially?Solution
Let the net bonus amount received by its full time employees in the beginning be Rs. x and n be the no. of employees working as freelancers.
Bonus amount distributed among employees in the beginning = 8x
Now, when the bonus received by each employee decreased by Rs. 150,
8x/(8 + n) = x - 150
8 + n = 8x/(x-150) ..(1)
Again, bonus received by each employee after extra amount of 1320 was sanctioned by the director = Rs. 520
(8x + 1320)/(8 + n) = 520
8 + n = (8x + 1320)/520 ..(2)
Using equations (1) and (2),
8x/(x - 150) = (8x + 1320)/520
x/(x - 150) = (x + 165)/520
520x = (x - 150)(x + 165)
x 2 - 505x - 24750 = 0
x = 550 or -45
As x cannot be negative, so, x = 550
Hence, net bonus amount received by its full time employees in the beginning = Rs. 550
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