Mathematics for FinancePYQ Nov 18Question 1183 of 512
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A certain sum of money Q\displaystyle Q was deposited for 5\displaystyle 5 years and 4\displaystyle 4 months at 4.5%\displaystyle 4.5\% simple interest and amounted to Rs. 248\displaystyle \text{Rs. }248, then the value of Q\displaystyle Q is

Options

ARs. 200\displaystyle \text{Rs. }200
BRs. 210\displaystyle \text{Rs. }210
CRs. 220\displaystyle \text{Rs. }220
DRs. 240\displaystyle \text{Rs. }240
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Correct Answer

✅ Option a — Rs. 200\displaystyle \text{Rs. }200

All Options:

  • ARs. 200\displaystyle \text{Rs. }200
  • BRs. 210\displaystyle \text{Rs. }210
  • CRs. 220\displaystyle \text{Rs. }220
  • DRs. 240\displaystyle \text{Rs. }240

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - Amount (A\displaystyle A) = Rs. 248\displaystyle \text{Rs. }248 - Time (t\displaystyle t) = 5\displaystyle 5 years and 4\displaystyle 4 months = 5+412=5+13=163\displaystyle 5 + \frac{4}{12} = 5 + \frac{1}{3} = \frac{16}{3} years - Simple Interest Rate (r\displaystyle r) = 4.5%\displaystyle 4.5\% per annum **Step 1: Set up the Simple Interest Amount equation** A=Q(1+r×t100)A = Q\left(1 + \frac{r \times t}{100}\right) 248=Q(1+4.5×163100)248 = Q\left(1 + \frac{4.5 \times \frac{16}{3}}{100}\right) **Step 2: Simplify the term inside the parenthesis** Interest component=4.5×163×100=1.5×16100=24100=0.24\text{Interest component} = \frac{4.5 \times 16}{3 \times 100} = \frac{1.5 \times 16}{100} = \frac{24}{100} = 0.24 248=Q(1+0.24)248 = Q(1 + 0.24) 248=1.24Q248 = 1.24 Q **Step 3: Solve for Q\displaystyle Q** Q=2481.24=Rs. 200Q = \frac{248}{1.24} = \text{Rs. }200 Hence, **Option A** is the correct answer.

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