Mathematics for FinanceMTP Dec 23 Series IQuestion 1395 of 512
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The SI on sum of money at 6%\displaystyle 6\% p.a for 7 years is equal to twice of SI on another sum for 9 years at 5%\displaystyle 5\% p.a. The ratio will be

Options

A2:15\displaystyle 2:15
B7:15\displaystyle 7:15
C15:7\displaystyle 15:7
D1:7\displaystyle 1:7
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Correct Answer

✅ Option c — 15:7\displaystyle 15:7

All Options:

  • A2:15\displaystyle 2:15
  • B7:15\displaystyle 7:15
  • C15:7\displaystyle 15:7
  • D1:7\displaystyle 1:7

Detailed Solution & Explanation

**Derivation of Ratio of Principals** Given: - Let the first principal be P1\displaystyle P_1 and the second principal be P2\displaystyle P_2. - Rate for first sum (R1\displaystyle R_1) = 6%\displaystyle 6\% p.a. - Time for first sum (T1\displaystyle T_1) = 7\displaystyle 7 years - Rate for second sum (R2\displaystyle R_2) = 5%\displaystyle 5\% p.a. - Time for second sum (T2\displaystyle T_2) = 9\displaystyle 9 years - Condition: SI1=2SI2\displaystyle SI_1 = 2 SI_2 **Step 1: Write Simple Interest formulas** SI1=P1×R1×T1100=P1×6×7100=42P1100SI_1 = \frac{P_1 \times R_1 \times T_1}{100} = \frac{P_1 \times 6 \times 7}{100} = \frac{42 P_1}{100} SI2=P2×R2×T2100=P2×5×9100=45P2100SI_2 = \frac{P_2 \times R_2 \times T_2}{100} = \frac{P_2 \times 5 \times 9}{100} = \frac{45 P_2}{100} **Step 2: Apply the given condition** 42P1100=2(45P2100)\frac{42 P_1}{100} = 2 \left(\frac{45 P_2}{100}\right) 42P1=90P242 P_1 = 90 P_2 P1P2=9042=157\frac{P_1}{P_2} = \frac{90}{42} = \frac{15}{7} Hence, **Option C** is the correct answer.

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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