CAT 2023 Slot 2 · Quant · Question 8
CAT 2023 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.
- A4 : 5
- B5 : 6
- C5 : 4
- D6 : 5
Answer & solution
Answer: Option A
Take the company as 100 employees with a total salary bill of 600 units, chosen so the fractions stay whole.
Manufacturing employs 20% of them, that is 20 people, leaving 80 in other departments.
Manufacturing earns one-sixth of the total, that is \frac{600}{6}=100 units.
The non-manufacturing employees therefore earn 600-100=500 units.
The manufacturing average is \frac{100}{20}=5 units per person.
The non-manufacturing average is \frac{500}{80}=6.25 units per person.
The ratio is 5:6.25, and multiplying both sides by 4 gives 20:25.
Dividing by 5, the ratio is 4:5 — the first option.
Shortcut. Average is total divided by headcount, so the ratio of averages is the ratio of salary shares divided by the ratio of headcount shares. That is \frac{1/6}{5/6}\div \frac{20}{80}=\frac{1}{5}\div \frac{1}{4}=\frac{4}{5} in one line.
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