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CAT 2023 Slot 2 — QA Question 13

RatioEasy

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employ

Answer & solution

  • 4 : 5

  • B

    6 : 5

  • C

    5 : 6

  • D

    5 : 4

Solution

Easy

Assume convenient numbers: 100100 employees and total salary 600600 (a multiple of 66 to keep fractions clean). Split into 2020 manufacturing and 8080 non-manufacturing, use the "one-sixth" condition to get each group's total, then divide by headcount for the averages.

1

Set up the counts and totals. Take 100100 employees and total salary =600=600:

Manufacturing=20%×100=20 peopleNon-manufacturing=80 people\begin{aligned} &\text{Manufacturing}=20\%\times100=20\ \text{people}\\ &\text{Non-manufacturing}=80\ \text{people} \end{aligned}
2

Split the total salary. Manufacturing earns one-sixth, the rest earns five-sixths:

Manufacturing total=16×600=100Non-manufacturing total=600−100=500\begin{aligned} &\text{Manufacturing total}=\tfrac{1}{6}\times600=100\\ &\text{Non-manufacturing total}=600-100=500 \end{aligned}
3

Average == total ÷\div count for each group:

Manufacturing avg=10020=5Non-manufacturing avg=50080=6.25\begin{aligned} &\text{Manufacturing avg}=\frac{100}{20}=5\\ &\text{Non-manufacturing avg}=\frac{500}{80}=6.25 \end{aligned}
4

Take the ratio:

5:6.25=56.25=45=4:5\begin{aligned} &5:6.25=\frac{5}{6.25}=\frac{4}{5}=4:5 \end{aligned}

The required ratio is 4:5\mathbf{4:5}.

Ratio of averages =salary sharepeople share=\dfrac{\text{salary share}}{\text{people share}} for each group, so it is 1/620/100:5/680/100=56:2524=4:5\dfrac{1/6}{20/100}:\dfrac{5/6}{80/100}=\dfrac{5}{6}:\dfrac{25}{24}=4:5. No assumed numbers needed.

CAT 2023 Slot 2 QA Q13: In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all t — Solution | TheCATExam