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8 men can complet a piece of work in 20 days. 8 women can do the same work in 32 days. In how many days will 5 men and 8 women together will complete the same work?

All I have is:

Men's one day work = 1/20

Women's one day work = 1/32

Together, 5/20 + 8/32 = 1/2

But 2 days is the wrong answer. The correct answer is 16.

How are these types of questions solved? What is the general trick and mental picture to form?

user1502
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2 Answers2

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You forgot the 8 men and 8 women.

A man's work in 1 day: 1/160.

A woman's work in 1 day: 1/256.

Then continue using your method.

KittyL
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  • Ah ok, thanks! And what is the general idea behind these types of questions? – user1502 Feb 01 '15 at 19:01
  • I think you already got the general idea. I would just do what you did. – KittyL Feb 01 '15 at 19:06
  • The general idea is that rates of "work completed" can be added together. You want to use the information given to find the rate at which each individual could complete the task, expressed as $ \ \frac{1 \ \text{(for the entire task)}}{\text{number of time units}} \ $ , the time unit often being days in these problems. – colormegone Feb 01 '15 at 19:12
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Ratio of efficiency of men to women = (8*32)/(8*20) = 8:5 Total work for women = 8*32 5 men will be equal to = 5*8/5 = 8 women so in 2nd case total women = 8 women + 5 men = 8 women + 8 women = 16 women number of days required = d so d*16 = 8*32 d = 16 days

Kouts Km
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