CAT 2022 Slot 2 · Quant · Question 5

CAT 2022 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceMedium
Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be
  1. A
    4200
  2. B
    4400
  3. C
    4300
  4. D
    4350
Pick an option, then check.
Answer & solution

Answer: Option B

An average saving of ₹550 across twelve months means a yearly total of 550\times 12=6600.

In each of the first nine months he earns ₹4000 and spends ₹3500.

So he saves 4000-3500=500 a month over that stretch.

Across nine months that is 500\times 9=4500.

The remaining three months must therefore supply 6600-4500=2100.

That is \frac{2100}{3}=700 of saving per month.

From the tenth month his expense is ₹3700.

So his earnings must be 3700+700=4400, that is ₹4400 — the second option.

Shortcut. Work in shortfalls: the target is ₹550 a month but the first nine months save ₹500, leaving a shortfall of ₹50 each, or ₹450 in all. That must be made up over three months, so those months need 550+150=700 of saving, hence earnings of 3700+700.

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