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CAT 2020 Slot 3 — QA Question 5

Man Days (single group of people)Easy

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

Answer & solution

Correct answer: 40

Answer: 40

Solution

Easy

Find the work rate from the first phase, scale it to the remaining work and remaining days, and use the proportion (men ×\times days) == constant for a fixed amount of work.

1

Work done so far. In 6060 days, 1.51.5 km of 66 km is built.

Fraction done=1.56=14\begin{aligned} &\text{Fraction done}=\frac{1.5}{6}=\frac{1}{4} \end{aligned}
2

Days the original crew would still need. The 140140 men did 14\tfrac14 of the work in 6060 days, so the whole job at that pace takes 4×60=2404\times60=240 days; the remaining 34\tfrac34 would take the same crew 240−60240-60 more days.

Days needed by 140 men=240−60⇒ Days needed=180\begin{aligned} &\text{Days needed by }140\text{ men}=240-60\\ &\Rightarrow\ \text{Days needed}=180 \end{aligned}
3

Days actually available.

Days left=200−60⇒ Days left=140\begin{aligned} &\text{Days left}=200-60\\ &\Rightarrow\ \text{Days left}=140 \end{aligned}
4

Apply men ×\times days == constant. The same remaining work: 140140 men over 180180 days equals (140+x)(140+x) men over 140140 days.

140×180=(140+x)×140⇒ 180=140+x(divide both sides by 140)⇒ x=40\begin{aligned} &140\times180=(140+x)\times140\\ &\Rightarrow\ 180=140+x \quad\text{(divide both sides by }140)\\ &\Rightarrow\ x=40 \end{aligned}
40 additional people40\ \text{additional people}

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CAT 2020 Slot 3 QA Q5: A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, — Solution | TheCATExam