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The time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job. Each man is twice as fast as a woman. How long will 12 men, 10 children and 8 women take to complete a job, given that a child would finish the job in 20 days?

The time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job. Each man is twice as fast as a woman. How long will 12 men, 10 children and 8 women take to complete a job, given that a child would finish the job in 20 days? Correct Answer 1 day

Short trick:

Let the efficiency of 1 man, 1 women and 1 child be m, w and c respectively.

2 × 4m = 5 c

⇒ 8 m = 5 c

⇒ m : c = 5 : 8

⇒ w = 5/2 = 2.5

Total work = 8 × 20 = 160

Total work done by 12 men, 8 women, 10 children in 1 days = 12 × 5 + 8 × 2.5 + 10 × 8 = 160

Required days = 160/160 = 1 day

Detailed method:

1 child can finish the job in = 20 days

5 child can finish the job in = 20/5 = 4 days

10 children can finish is the job in = 2 days

4 men can finish the job in = 4 × 2 = 8 days

12 men can finish the job in = 8/3 days

4 women can finish the job in = 8 × 2 = 16 days

8 women can finish the job in = 8 days

12 men, 8 women and 10 children complete the whole work in = 3/8 + 1/8 + 1/2 = (3 + 1 + 4)/8 = 8/8 = 1 days

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