Discussion

Question:

A group of N people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of N is

Explanation:

Let the efficiency of each person be ‘e’ units/hour.

Given,
35% work is done by N men in 10 days working for 7 hours/day, while
65% work is done by N-10 men in 14 days working for 10 hours/day

⇒ $\frac{\mathrm{N}\times 10\times 7}{0.35}$= $\frac{(\mathrm{N}-10)\times 14\times 10}{0.65}$

⇒ $\frac{\mathrm{N}\times 7}{7}$= $\frac{(\mathrm{N}-10)\times 14}{13}$

⇒ N = $\frac{(\mathrm{N}-10)\times 14}{13}$

⇒ 13N = 14N – 140

⇒ N = 140

Hence, option (b).

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