CAT 2022Slot 2QAQuestion & Solution
Question
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
Options
4400
4200
4300
4350
Solution
1. Concept Used
- Topic: Averages & Linear Equations (Monthly Savings Planning)
- Formula: $$ \text{Total Savings} = \text{Average Monthly Savings} \times 12 $$ $$ \text{Monthly Savings} = \text{Monthly Earnings} - \text{Monthly Expenses} $$
2. Calculation
Manu's yearly savings target is based on an average of ₹550 per month over 12 months.
$$\text{Total Savings Target} = 550 \times 12 = ₹6600$$
In the first 9 months, his earnings were ₹4000 and expenses were ₹3500, so monthly savings = ₹500.
$$\text{Savings in first 9 months} = 9 \times (4000 - 3500) = 9 \times 500 = ₹4500$$
The remaining savings required from the last 3 months (months 10, 11, 12):
$$\text{Savings needed in last 3 months} = 6600 - 4500 = ₹2100$$
This must be spread equally over the 3 remaining months:
$$\text{Monthly savings required} = \frac{2100}{3} = ₹700$$
Since his monthly expenses from the 10th month onward are ₹3700, his required monthly earnings are:
$$\text{Required monthly earnings} = 3700 + 700 = ₹4400$$
3. Solution
Answer = Option A ✅
The final calculated value is ₹4400. Manu must earn ₹4400 per month from the 10th month onward to meet his annual savings target of ₹6600.