Question

What sum of money will amount to Rs. 520 in 5 years and to Rs 568 in 7 years on simple interest?

• A. \( \text{Rs. } 400 \)
• B. \( \text{Rs. } 120 \)
• C. \( \text{Rs. } 510 \)
• D. \( \text{Rs. } 220 \)

Hint:

\textbf{Simple Interest Problems.} In simple interest, the interest earned is the same for each time period. The difference in the amounts over a different number of years can be used to find the interest earned in that additional time, which can then help determine the principal and the rate of interest.

Answer 1

The Correct Option is A

Let the principal sum of money be \(P\) and the rate of simple interest be \(R\) per annum. According to the formula for simple interest, the amount \(A\) after \(T\) years is given by: $$ A = P + \frac{P \times R \times T}{100} $$ From the problem statement, we have two conditions: (A) Amount after 5 years is Rs. 520: $$ 520 = P + \frac{P \times R \times 5}{100} \quad \cdots (A) $$ (B) Amount after 7 years is Rs. 568: $$ 568 = P + \frac{P \times R \times 7}{100} \quad \cdots (2) $$ Subtracting equation (A) from equation (2), we get: $$ 568 - 520 = \left( P + \frac{7PR}{100} \right) - \left( P + \frac{5PR}{100} \right) $$ $$ 48 = \frac{7PR}{100} - \frac{5PR}{100} $$ $$ 48 = \frac{2PR}{100} $$ $$ 48 = \frac{PR}{50} $$ $$ PR = 48 \times 50 = 2400 \quad \cdots (3) $$ Now, substitute the value of \(PR\) from equation (3) into equation (A): $$ 520 = P + \frac{5 \times 2400}{100} $$ $$ 520 = P + \frac{12000}{100} $$ $$ 520 = P + 120 $$ $$ P = 520 - 120 $$ $$ P = 400 $$ So, the sum of money (principal) is Rs. 400. We can also find the rate of interest \(R\) using equation (3): $$ 400 \times R = 2400 $$ $$ R = \frac{2400}{400} = 6 $$ Let's verify with the second condition: Amount after 7 years \( = 400 + \frac{400 \times 6 \times 7}{100} = 400 + 168 = 568 \). This matches the given information. Therefore, the sum of money is Rs. 400.