Work Equivalence with Changing Workers

CAT 2022 Slot 3 · QA · Easy · Arithmetic

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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

  1. A.

    23

  2. B.

    140

  3. C.

    36

  4. D.

    150

Answer

B

Explanation

Use the work formula: M1×D1×H1W1=M2×D2×H2W2\frac{M_1 \times D_1 \times H_1}{W_1} = \frac{M_2 \times D_2 \times H_2}{W_2}

Given:

  • M1=NM_1 = N, D1=10D_1 = 10, H1=7H_1 = 7, W1=35%=0.35W_1 = 35\% = 0.35
  • M2=N−10M_2 = N - 10, D2=14D_2 = 14, H2=10H_2 = 10, W2=65%=0.65W_2 = 65\% = 0.65

N×10×70.35=(N−10)×14×100.65\frac{N \times 10 \times 7}{0.35} = \frac{(N - 10) \times 14 \times 10}{0.65} 70N0.35=140(N−10)0.65\frac{70N}{0.35} = \frac{140(N - 10)}{0.65} 200N=280013(N−10)200N = \frac{2800}{13}(N - 10) 200N140=N−100.65\frac{200N}{140} = \frac{N - 10}{0.65} 100N0.35×100  ⟹  200N=140(N−10)0.65\frac{100N}{0.35 \times 100} \implies 200N = \frac{140(N - 10)}{0.65} Simplifying: 200N=215.38(N−10)…200N = \frac{215.38(N - 10)}{\dots} Let's re-simplify: 200N×0.65=140(N−10)200N \times 0.65 = 140(N - 10) 130N=140N−1400130N = 140N - 1400 10N=1400  ⟹  N=14010N = 1400 \implies N = 140.

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