Mathematics for FinancePYQ Jan 21Question 1212 of 512
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A certain sum amounted to 575\displaystyle 575 at 5%\displaystyle 5\% in a time in which 750\displaystyle 750 amounted to 840\displaystyle 840 at 4%\displaystyle 4\%. If the rate of interest is simple, find the sum -

Options

A525\displaystyle 525
B550\displaystyle 550
C515\displaystyle 515
D500\displaystyle 500
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Correct Answer

✅ Option d — 500\displaystyle 500

All Options:

  • A525\displaystyle 525
  • B550\displaystyle 550
  • C515\displaystyle 515
  • D500\displaystyle 500

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - For Case 1: Principal = P\displaystyle P, Rate = 5%\displaystyle 5\% S.I., Amount = Rs. 575\displaystyle \text{Rs. }575 in time t\displaystyle t. - For Case 2: Principal = Rs. 750\displaystyle \text{Rs. }750, Rate = 4%\displaystyle 4\% S.I., Amount = Rs. 840\displaystyle \text{Rs. }840 in time t\displaystyle t. **Step 1: Calculate time (t\displaystyle t) from Case 2** Simple Interest earned in Case 2=A2−P2=840−750=Rs. 90\text{Simple Interest earned in Case 2} = A_2 - P_2 = 840 - 750 = \text{Rs. }90 Using the Simple Interest formula: SI2=P2×r2×t100SI_2 = \frac{P_2 \times r_2 \times t}{100} 90=750×4×t10090 = \frac{750 \times 4 \times t}{100} 90=30t  ⟹  t=3 years90 = 30 t \implies t = 3 \text{ years} **Step 2: Solve for Case 1 principal (P\displaystyle P) with t=3\displaystyle t = 3 years** A1=P(1+r1×t100)A_1 = P\left(1 + \frac{r_1 \times t}{100}\right) 575=P(1+5×3100)575 = P\left(1 + \frac{5 \times 3}{100}\right) 575=P(1+0.15)575 = P(1 + 0.15) 575=1.15P575 = 1.15 P P=5751.15=Rs. 500P = \frac{575}{1.15} = \text{Rs. }500 Hence, **Option D** is the correct answer.

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