Question

There was a big businessman who hired men, women, and children to work on his construction site. A man does twice the work as a woman in a day whereas a child does one-third the work as a woman in a day. The businessman hired 39 pairs of hands in the ratio of 6 : 5 : 2 with the number of men being the most and the number of children being the least. They were paid Rs 11130. How much was a child paid if the amount paid was in proportion to the amount of work done?
1. 50
2. 420
3. 70
4. 140

Answer 1

Correct Answer - Option 3 : 70

CONCEPT:

We need to express the efficiency of men and children in terms of the women

CALCULATION:

Let the number of men be 6x, women be 5x and children be 2x 

∵ total number of people be 39 

∴ 13x = 39 

⇒  x = 3

∴ number of men = 18; women = 15; children = 6

The ratio of work done by men: women: children = 6: 3 : 1

The ratio of work done by 18 men: 15 women: 6 children = 108: 45 : 6

Hence children would get  \( 6 \times 11130\over(108+45+6) \) = 420

 ∴ one child would get 420/6 = Rs.70

The biggest mistake people make after such a big calculation is that they forget to divide the amount received by the number of people, in this case, the number of children.