Question
In a company, there are men, women, and boys working.
The total daily payment to all workers is Rs. 6,390. The number of men is 20% more than the number of women, and the number of boys is 40% less than the number of women. A woman's wage is 137.5% of a man's wage, and a boy's wage is 162.5% of a man's wage. If there are 12 men working in the company, what is the difference between the total wages of 30 women and 30 boys?Solution
Let the no. of women in company = x
So, the no. of men in company = x*120/100 = 1.2x
And the no. of boys in company = x*60/100 = 0.6x
Now given that, 1.2x = 12 => x = 10
The no. of men, women and boys in the company is 1.2*10 = 12, 1*10 = 10 and 0.6x*10 = 6 respectively.
Let the share of a man = y
So, the share of a woman = 137.5y/100 = 1.375y
And the share of a boy = 162.5y/100 = 1.625y
Ratio between the share of a man, a woman and a boy = y: 1.375y: 1.625y = 8: 11: 13
The ratio between the shares of 12 men, 10 women and 6 boys-
=> 12*8: 10*11: 6*13
=> 96: 110: 78
=> 48: 55: 39
The share of 10 women = (55/142)*6390 = 2475
The share of 30 women = (2475/10)*30 = 7425
The share of 6 boys = (39/142)*6390 = 1755
The share of 30 boys = (1755/6)*30 = 8775
Required difference = 8775 - 7425 = 1350
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