Road construction workforce

CAT 2020 Slot 3 · QA · Easy · Time and work

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A contractor agreed to construct a 6 km6\text{ km} road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km1.5\text{ km} road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Answer

40

Explanation

Work done in 60 days by 140 persons = 1.5 km1.5\text{ km}. Remaining work = 6−1.5=4.5 km6 - 1.5 = 4.5\text{ km}. Remaining time = 200−60=140200 - 60 = 140 days.

Using M1D1W1=M2D2W2\frac{M_1 D_1}{W_1} = \frac{M_2 D_2}{W_2}: 140×601.5=M2×1404.5\frac{140 \times 60}{1.5} = \frac{M_2 \times 140}{4.5} 140×60×3=M2×140  ⟹  M2=180140 \times 60 \times 3 = M_2 \times 140 \implies M_2 = 180.

Additional people needed = 180−140=40180 - 140 = 40.

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