a company offered its 350 employees a bonus of rs 10 to each male and rs 8.15 to each female. all the females accepted but a certain percentage of males refused to accept. the total bonus paid was independent of the number of males. what was the total amount paid to the females (in rupees)?
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Let the total number of males be m.
Let p% be the number of males who refused the bonus.
Let the total bonus paid be Rs T.
T = 10(1 - p/100)m + 8.15(350 - m)
10m - 0.1pm0.1 pm + 2852.5 - 8.15m = T
The total bonus is independent of males therefore :
10m = 0.1pm + 8.15m or 0.1pm = 1.85
p = 18.5%
The number of males who have refused must be an integer.
It is only possible when m = 200 out of 350.
If m were 100 then the males who refused would be 18.5 and this is not possible.
The number of females is thus :
350 - 200 = 150
The total bonus paid to females is thus :
150 × 8.15 = 1222.5
Rs 1222.5
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