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Directions : Read the following information carefully and answer the questions. x women can complete a piece of work in 2y days. 1.5x men can complete the same work in y days while 2x children can complete the same work in 3y days. 8 women, 8 children and 8 men together can complete same work in 22 1/2 days. 9 men can complete the same work in (y + 20) days.
What is the value of y.
14
18
20
16
24
- Let's break down the information given:
- x women can complete the work in 2y days.
- 1.5x men can complete it in y days.
- 2x children can complete it in 3y days.
- Combined work capacity:
- The work done by 1 woman in 1 day = 1 / (2y) of the total work.
- The work done by 1 man in 1 day = 1 / (1.5y) of the total work.
- The work done by 1 child in 1 day = 1 / (6y) of the total work.
- For 8 women, 8 children, and 8 men:
- The work done together in 1 day = 8*(1/2y) + 8*(1/6y) + 8*(1/1.5y) of the total work.
- This completes the work in 22.5 days.
- For 9 men:
- The work done by 9 men in 1 day = 9 / (1.5y) of the total work.
- They complete the work in (y + 20) days.
- Solving for y, we find that it equals 24.
Therefore, the correct answer is:
Option: 5, 24
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