Mathematics for FinanceMTP Jun 23 Series IIQuestion 1381 of 512
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Mr. A invested X\displaystyle X in an organization, it amounts to 150\displaystyle 150 at 5%\displaystyle 5\% p.a. S.I. and to 100\displaystyle 100 at 3%\displaystyle 3\% p.a. S.I. Then the value of X\displaystyle X is

Options

A70\displaystyle 70
B40\displaystyle 40
C25\displaystyle 25
DNone of these
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Correct Answer

✅ Option c — 25\displaystyle 25

All Options:

  • A70\displaystyle 70
  • B40\displaystyle 40
  • C25\displaystyle 25
  • DNone of these

Detailed Solution & Explanation

**Derivation of Principal Investment Value** Given: - Amount at 5%\displaystyle 5\% p.a. simple interest = Rs. 150\displaystyle \text{Rs. }150 - Amount at 3%\displaystyle 3\% p.a. simple interest = Rs. 100\displaystyle \text{Rs. }100 - Let X\displaystyle X be the principal sum and t\displaystyle t be the time period in years. **Step 1: Formulate the equations for both cases** 150=X(1+0.05t)— (Equation 1)150 = X(1 + 0.05 t) \quad \text{--- (Equation 1)} 100=X(1+0.03t)— (Equation 2)100 = X(1 + 0.03 t) \quad \text{--- (Equation 2)} **Step 2: Divide Equation 1 by Equation 2** 150100=1+0.05t1+0.03t\frac{150}{100} = \frac{1 + 0.05 t}{1 + 0.03 t} 1.5(1+0.03t)=1+0.05t1.5(1 + 0.03 t) = 1 + 0.05 t 1.5+0.045t=1+0.05t1.5 + 0.045 t = 1 + 0.05 t 0.5=0.005t  ⟹  t=0.50.005=100 years0.5 = 0.005 t \implies t = \frac{0.5}{0.005} = 100 \text{ years} **Step 3: Solve for X\displaystyle X** Substitute t=100\displaystyle t = 100 into Equation 2: 100=X(1+0.03×100)100 = X(1 + 0.03 \times 100) 100=X(1+3)100 = X(1 + 3) 100=4X  ⟹  X=1004=Rs. 25100 = 4 X \implies X = \frac{100}{4} = \text{Rs. }25 *(Note: The database lists Option A (70\displaystyle 70) as correct, which is a typo in the key. The mathematically correct principal is 25, which is Option C.)* Hence, **Option C** is the correct answer.

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