Mathematics for FinancePYQ Nov 19Question 1196 of 512
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A man invests Rs. 12,000\displaystyle \text{Rs. }12,000 at 10%\displaystyle 10\% p.a. and another sum of money at 20%\displaystyle 20\% p.a. for one year. The total investment earns at 14%\displaystyle 14\% p.a. simple interest the total investment is:

Options

ARs. 8,000\displaystyle \text{Rs. }8,000
BRs. 20,000\displaystyle \text{Rs. }20,000
CRs. 14,000\displaystyle \text{Rs. }14,000
DRs. 16,000\displaystyle \text{Rs. }16,000
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Correct Answer

✅ Option b — Rs. 20,000\displaystyle \text{Rs. }20,000

All Options:

  • ARs. 8,000\displaystyle \text{Rs. }8,000
  • BRs. 20,000\displaystyle \text{Rs. }20,000
  • CRs. 14,000\displaystyle \text{Rs. }14,000
  • DRs. 16,000\displaystyle \text{Rs. }16,000

Detailed Solution & Explanation

**Derivation of Total Investment from Combined Simple Interest Rate** Given: - Investment 1 (P1\displaystyle P_1) = Rs. 12,000\displaystyle \text{Rs. }12,000 at rate r1=10%\displaystyle r_1 = 10\% p.a. - Investment 2 (P2\displaystyle P_2) = S\displaystyle S (unknown sum) at rate r2=20%\displaystyle r_2 = 20\% p.a. - Time (t\displaystyle t) = 1\displaystyle 1 year - Overall average interest rate earned = 14%\displaystyle 14\% p.a. **Step 1: Express total interest earned** Interest from P1=12000×10×1100=Rs. 1,200\text{Interest from } P_1 = \frac{12000 \times 10 \times 1}{100} = \text{Rs. }1,200 Interest from P2=S×20×1100=0.20S\text{Interest from } P_2 = \frac{S \times 20 \times 1}{100} = 0.20 S Total Interest Earned=1200+0.20S\text{Total Interest Earned} = 1200 + 0.20 S **Step 2: Express interest using the average rate on total investment (P1+P2\displaystyle P_1 + P_2)** Total Interest=(12000+S)×14×1100=0.14(12000+S)=1680+0.14S\text{Total Interest} = \frac{(12000 + S) \times 14 \times 1}{100} = 0.14(12000 + S) = 1680 + 0.14 S **Step 3: Equate the two expressions and solve for S\displaystyle S** 1200+0.20S=1680+0.14S1200 + 0.20 S = 1680 + 0.14 S 0.20S−0.14S=1680−12000.20 S - 0.14 S = 1680 - 1200 0.06S=4800.06 S = 480 S=4800.06=Rs. 8,000S = \frac{480}{0.06} = \text{Rs. }8,000 **Step 4: Find the total investment** Total Investment=P1+P2=12000+8000=Rs. 20,000\text{Total Investment} = P_1 + P_2 = 12000 + 8000 = \text{Rs. }20,000 Hence, **Option B** is the correct answer.

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