Multiple choice

In the following questions three equations numbered I, II and III are given. You have to solve all the equations either together or separately, or two together and one separately, or by any other method. A man can complete a piece of work in 8 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. x = If 5 men, 4 women and 10 children work together, in how many days can the work be completed y = If 4 men, 5 women and 10 children work together, in how many days can the work be completed z = If 3 men, 4 women and 12 children work together, in how many days can the work be completed

  1. x < y < z

  2. x > y > z

  3. x > y = z

  4. x z

  5. Relationship cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

One man's rate is 1/8 work per day, one woman's rate is 1/16, and one child's rate is 1/20. The combined rates for x, y, and z are 1.375, 1.3125, and 1.225 work per day respectively. Higher rate means fewer days, so x < y < z.

AI explanation

By converting all work capacities to child-equivalents, we find that one man does the work of 10 children and one woman does the work of 8 children. For x, the team of 5 men, 4 women and 10 children equals a capacity of 92 children. For y, the team of 4 men, 5 women and 10 children equals a capacity of 90 children. For z, the team of 3 men, 4 women and 12 children equals a capacity of 88 children. Since the total work is constant, a higher capacity means fewer days, which shows that x takes the least time and z takes the most time, confirming the order x < y < z.

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