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Let ‘m’ be the number of males, and let ‘x’ be the fraction of males refusing the bonus. Then the total bonus paid T= 8.15(350-m)+10(1-x)m
= 2852.5+m(1.85-10x),which will be independent of m only if x=0.185; so T=2852.5
Now, number of males refusing bonus= 0.185m, which has to be a +ve integer
Therefore 185m/1000 is a +ve integer or 185/(1000/m) is a +ve integer. 1000/m =37 or 5. 37 not possible; so 1000/m=5, which gives m=200. Thus females=150. Bonus paid to females= 8.15*150=1222.5
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 number of persons who do not take any juice and the number of persons who take all 4 types of juices be ‘x’.
As there are ‘x’ people who take atleast 4 types of juices there should be ‘2x’ people who take atleast 3 types of juices.
This means the number of people who take exactly 3 types of juices = 2x - x = x.
As there are ‘2x’ people who take atleast 3 types of juices there should be ‘4x’ people who take atleast 2 types of juices.
This means the number of people who take exactly 2 types of juices = 4x - x - x = 2x.
As there are ‘4x’ people who take atleast 2 types of juices there should be ‘8x’ people who take atleast 1 type of juices.
This means the number of people who take exactly 1 type of juices = 8x - 4x = 4x.
Thus the total number of people in the Gym = x + 4x + 2x + x + x = 9x.
9x = 207 => x = 23.
The number of people who take exactly 2 types of juices = 2x = 46.
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Let the number of persons who do not take any juice and the number of persons who take all 4 types of juices be ‘x’.
As there are ‘x’ people who take atleast 4 types of juices there should be ‘2x’ people who take atleast 3 types of juices.
This means the number of people who take exactly 3 types of juices = 2x - x = x.
As there are ‘2x’ people who take atleast 3 types of juices there should be ‘4x’ people who take atleast 2 types of juices.
This means the number of people who take exactly 2 types of juices = 4x - x - x = 2x.
As there are ‘4x’ people who take atleast 2 types of juices there should be ‘8x’ people who take atleast 1 type of juices.
This means the number of people who take exactly 1 type of juices = 8x - 4x = 4x.
Thus the total number of people in the Gym = x + 4x + 2x + x + x = 9x.
9x = 207 => x = 23.
The number of people who take exactly 2 types of juices = 2x = 46.
