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CAT 2022 Slot 3 — QA Question 3

Man Days (single group of people)Easy

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

Answer & solution

  • A

    23

  • 140

  • C

    36

  • D

    150

Solution

Easy

Work = (people)×\times(days)×\times(hours)×\times(efficiency). Set up the proportion: the first stretch did 35%35\% with NN people, the second did the remaining 65%65\% with N−10N-10 people. Equate "work per unit fraction" and solve for NN.

1

Write total man-hours for each phase (efficiency ee cancels later):

35%: N×10×7 man-hours65%: (N−10)×14×10 man-hours\begin{aligned} &35\%:\ N\times10\times7\ \text{man-hours}\\ &65\%:\ (N-10)\times14\times10\ \text{man-hours} \end{aligned}
2

Man-hours are proportional to work done, so:

N×10×70.35=(N−10)×14×100.65\frac{N\times10\times7}{0.35}=\frac{(N-10)\times14\times10}{0.65}
3

Simplify. Divide both sides by 1010 and clear the decimals (0.35,0.65→7,130.35,0.65\to7,13):

7N7=14(N−10)13N=14(N−10)1313N=14N−140N=140\begin{aligned} &\frac{7N}{7}=\frac{14(N-10)}{13}\\ &N=\frac{14(N-10)}{13}\\ &13N=14N-140\\ &N=140 \end{aligned}
N=140N=\mathbf{140}
CAT 2022 Slot 3 QA Q3: A group of N people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days — Solution | TheCATExam