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CAT 2024 Slot 1 — QA Question 3

Man Days (single group of people)Easy

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to  complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

Answer & solution

Answer: 6

Solution

Medium

Measure the task in person-hours. Renu's and Seema's total-hour capacities give their hourly rates. Then translate the day/hour agreement into actual hours each puts in, and split the one unit of work between them.

1

Find each person's hourly rate. Renu finishes in 15×4=6015\times4=60 hours; Seema in 8×5=408\times5=40 hours.

Renu’s rate=160 task/hour⇒ Seema’s rate=140 task/hour\begin{aligned} &\text{Renu's rate}=\dfrac{1}{60}\ \text{task/hour}\\ &\Rightarrow\ \text{Seema's rate}=\dfrac{1}{40}\ \text{task/hour} \end{aligned}
2

Apply the working agreement. Renu works 22 hours/day, so Seema works double =4=4 hours/day. Let Seema work ss days; then Renu works double =2s=2s days.

Renu’s hours=2×(2s)=4s⇒ Seema’s hours=4×s=4s\begin{aligned} &\text{Renu's hours}=2\times(2s)=4s\\ &\Rightarrow\ \text{Seema's hours}=4\times s=4s \end{aligned}
3

Total work must equal one task. Combine the hours from step 2 with the rates from step 1.

4s60+4s40=1⇒ s15+s10=1(simplify each term)⇒ 2s+3s30=1(common denominator 30)⇒ 5s=30⇒ s=6\begin{aligned} &\dfrac{4s}{60}+\dfrac{4s}{40}=1\\ &\Rightarrow\ \dfrac{s}{15}+\dfrac{s}{10}=1 \quad\text{(simplify each term)}\\ &\Rightarrow\ \dfrac{2s+3s}{30}=1 \quad\text{(common denominator 30)}\\ &\Rightarrow\ 5s=30\\ &\Rightarrow\ s=6 \end{aligned}
Seema works 6 days\text{Seema works }6\text{ days}
CAT 2024 Slot 1 QA Q3: Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days wor — Solution | TheCATExam