Mathematics for FinancePYQ Nov 19Question 1370 of 512
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The difference in simple interest of a sum invested of Rs. 1,500\displaystyle \text{Rs. }1,500 for 3\displaystyle 3 years is Rs. 18\displaystyle \text{Rs. }18. The difference in their rates is

Options

A0.4\displaystyle 0.4
B0.6\displaystyle 0.6
C0.8\displaystyle 0.8
D0.10\displaystyle 0.10
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Correct Answer

✅ Option a — 0.4\displaystyle 0.4

All Options:

  • A0.4\displaystyle 0.4
  • B0.6\displaystyle 0.6
  • C0.8\displaystyle 0.8
  • D0.10\displaystyle 0.10

Detailed Solution & Explanation

**Derivation of Difference in Interest Rates** Given: - Principal (P\displaystyle P) = Rs. 1,500\displaystyle \text{Rs. }1,500 - Time (t\displaystyle t) = 3\displaystyle 3 years - Difference in Simple Interest = Rs. 18\displaystyle \text{Rs. }18 **Step 1: Set up the formula for difference in Simple Interest** Let the two rates be r1\displaystyle r_1 and r2\displaystyle r_2. SI1−SI2=P×r1×t100−P×r2×t100SI_1 - SI_2 = \frac{P \times r_1 \times t}{100} - \frac{P \times r_2 \times t}{100} 18=1500×(r1−r2)×310018 = \frac{1500 \times (r_1 - r_2) \times 3}{100} **Step 2: Solve for (r1−r2)\displaystyle (r_1 - r_2)** 18=15×3×(r1−r2)18 = 15 \times 3 \times (r_1 - r_2) 18=45(r1−r2)18 = 45 (r_1 - r_2) r1−r2=1845=25=0.4%r_1 - r_2 = \frac{18}{45} = \frac{2}{5} = 0.4\% Hence, **Option A** is the correct answer.

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