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Question 35
The time taken by 24 children to complete a project is twice the time taken by 16 women to complete the same project. If 28 women complete the project in 8 days, how many days will 28 women and 24 children together take to complete the project?
Solution
Time taken by 24 children is twice the time taken by 16 women to finish the same project.
Hence, 24 children's work can be completed by 8 women.
Work done by 1 woman in 1 day = $$\frac{1}{28\times 8}$$
Work done by 28 women and 24 children in 1 day = Work done by (28+8 = 36) women in 1 day
= $$\frac{36}{28 \times 8}$$
= $$\frac{9}{56}$$
$$\therefore$$ Number of days required by them = $$\frac{56}{9} = 6 \frac{2}{9}$$
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