Multiple choice

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?

  1. 4 days

  2. 3 days

  3. 2 days

  4. 1 day
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A child finishes in 20 days, so 1 child's rate is 1/20. 5 children take 4 days, so 4 men take 8 days (double time), meaning 1 man's rate is 1/32. Since 1 man is twice as fast as a woman, 1 woman's rate is 1/64. Total rate for 12 men, 10 children, 8 women = 12/32 + 10/20 + 8/64 = 3/8 + 1/2 + 1/8 = 1. The job takes 1/1 = 1 day.

AI explanation

Since one child finishes the job in 20 days, the total work is 20 child-days. Five children have a combined capacity of 1/4 of the job per day, taking 4 days, so 4 men taking double that time means 4 men take 8 days, establishing one man's capacity as 1/32 of the job per day. Because each man is twice as fast as a woman, one woman's capacity is 1/64 of the job per day. The combined daily capacity of 12 men (12/32), 10 children (10/20), and 8 women (8/64) equals 3/8 plus 1/2 plus 1/8, which totals 1. Therefore, the entire group completes the job in 1 day.

Keep practicing — related questions