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CAT 2019 Slot 1 — QA Question 16

Man Days (multiple groups of people)Easy

Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?

Answer & solution

Answer: 13

Solution

Easy

Let one man's daily work be xx and one machine's be yy. "Half the time" means the first team is twice as efficient, giving one linear relation between xx and yy. Convert "2 machines in 13 days" into men using that relation.

1

Translate the time condition. Half the time ⇒\Rightarrow double the rate.

3x+8y=2 (8x+3y)(rate inversely ∝ time)⇒ 3x+8y=16x+6y⇒ 13x=2y\begin{aligned} &3x+8y=2\,(8x+3y)\quad\text{(rate inversely }\propto\text{ time)}\\ &\Rightarrow\ 3x+8y=16x+6y\\ &\Rightarrow\ 13x=2y \end{aligned}
2

Interpret the relation. 1313 men's daily work equals 22 machines' daily work.

13x=2y(from step 1)⇒ 13 men/day=2 machines/day\begin{aligned} &13x=2y\quad\text{(from step 1)}\\ &\Rightarrow\ 13\text{ men/day}=2\text{ machines/day} \end{aligned}
3

Match the deadline. Same daily output ⇒\Rightarrow same number of days.

2 machines finish in 13 days⇒ 13 men finish in 13 days(equal rates, equal job)\begin{aligned} &2\text{ machines finish in }13\text{ days}\\ &\Rightarrow\ 13\text{ men finish in }13\text{ days}\quad\text{(equal rates, equal job)} \end{aligned}
Number of men=13\text{Number of men}=13
CAT 2019 Slot 1 QA Q16: Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish — Solution | TheCATExam