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Question:

A mother along with her two sons is entrusted with the task of cooking Biryani for a family get-together. It takes 30 minutes for all three of them cooking together to complete 50 percent of the task. The cooking can also be completed if the two sons start cooking together and the elder son leaves after 1 hour and the younger son cooks for further 3 hours. If the mother needs 1 hour less than the elder son to complete the cooking, how much cooking does the mother complete in an hour?

Explanation:

Let the number of days required to complete the work by mother, elder son and younger son be m, e and y hours respectively.

Therefore, work done by mother; elder son and younger son in one day is 1/m, 1/e and 1/n respectively.

Also m = e – 1 (∵ Mother take one hour less than the elder son)

Based on the conditions given,

$\frac{1}{m}$ + $\frac{1}{e}$ + $\frac{1}{y}$ = 1          ...(1)

$\frac{1}{e}$ + $\frac{1}{y}$ + $\frac{3}{y}$ = 1           ...(2)

$\frac{1}{y}$ = $\frac{e-1}{4e}$

Also m = e – 1

Substituting values of (1/m) and (1/y) in (1)

$\frac{1}{e-1}$ + $\frac{1}{e}$ + $\frac{e-1}{4e}$ = 1

Solving,

e = 3

Therefore, m = 2 and work done in 1 hour = 50%

Hence, option (b).