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CAT 2022 Slot 2 — QA Question 13

Simple EquationsEasy

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:

Answer & solution

  • 4400

  • B

    4300

  • C

    4200

  • D

    4350

Solution

Easy

Savings = income − expense, taken over the full year. Find the required total income for 12 months, subtract the known income of the first 9 months, then split what's left over the last 3 months.

1

Yearly savings target and yearly expense:

Savings=12×550=₹6,600Expense=9×3500⏟31,500+3×3700⏟11,100=₹42,600\begin{aligned} &\text{Savings}=12\times 550=\text{₹}6{,}600\\ &\text{Expense}=\underbrace{9\times 3500}_{31{,}500}+\underbrace{3\times 3700}_{11{,}100}=\text{₹}42{,}600 \end{aligned}
2

Required total yearly income = expense + savings:

42,600+6,600=₹49,20042{,}600+6{,}600=\text{₹}49{,}200
3

Subtract the first 9 months' income and split over 3 months:

Income(first 9)=9×4000=36,000Income(last 3)=49,200−36,000=13,200Monthly=13,2003=₹4,400\begin{aligned} &\text{Income(first 9)}=9\times 4000=36{,}000\\ &\text{Income(last 3)}=49{,}200-36{,}000=13{,}200\\ &\text{Monthly}=\tfrac{13{,}200}{3}=\text{₹}4{,}400 \end{aligned}
₹ 4400 per month\text{₹}\,\mathbf{4400}\text{ per month}
CAT 2022 Slot 2 QA Q13: Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine mon — Solution | TheCATExam