Mathematics for FinanceMTP Dec 23 Series IIQuestion 3953 of 507
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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Options

A4,000\displaystyle 4,000
B5,000\displaystyle 5,000
C6,000\displaystyle 6,000
DNone of these
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Correct Answer

Option b5,000\displaystyle 5,000

All Options:

  • A4,000\displaystyle 4,000
  • B5,000\displaystyle 5,000
  • C6,000\displaystyle 6,000
  • DNone of these

Detailed Solution & Explanation

Let the principal amount (sum of money) be P\displaystyle P. Let the initial rate of simple interest be r%\displaystyle r\% p.a. The interest earned in 2.5\displaystyle 2.5 years is: SI1=P×r×2.5100SI_1 = \frac{P \times r \times 2.5}{100} If the interest rate were 4%\displaystyle 4\% higher, the new rate would be (r+4)%\displaystyle (r + 4)\% p.a., and the interest earned would be: SI2=P×(r+4)×2.5100SI_2 = \frac{P \times (r + 4) \times 2.5}{100} The difference in simple interest is given as Rs. 500\displaystyle \text{Rs. }500: SI2SI1=500SI_2 - SI_1 = 500 P×(r+4)×2.5100P×r×2.5100=500\frac{P \times (r + 4) \times 2.5}{100} - \frac{P \times r \times 2.5}{100} = 500 P×2.5100×(r+4r)=500\frac{P \times 2.5}{100} \times (r + 4 - r) = 500 P×0.025×4=500P \times 0.025 \times 4 = 500 0.1P=5000.1P = 500 Solving for P\displaystyle P: P=5000.1=5,000P = \frac{500}{0.1} = 5,000 Thus, the sum of money is Rs. 5,000\displaystyle \text{Rs. }5,000. Hence, **Option B** is the correct answer.

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