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

Question

Accepted Answer

To find the principal amount:

1. **Calculate the interest for 2 years:**  
   The difference between the amounts in 7 years and 5 years is due to the interest for 2 years:  
   $$ 	ext{Interest for 2 years} = 568 - 520 = Rs. 48. $$

2. **Calculate the interest for 1 year:**  
   $$ 	ext{Interest for 1 year} = \frac{48}{2} = Rs. 24. $$

3. **Calculate the total interest for 5 years:**  
   $$ 	ext{Interest for 5 years} = 24 	imes 5 = Rs. 120. $$

4. **Find the principal amount:**  
   The amount after 5 years includes the principal and interest for 5 years:  
   $$ 	ext{Principal} = 	ext{Amount after 5 years} - 	ext{Interest for 5 years}. $$  
   Substituting values:  
   $$ 	ext{Principal} = 520 - 120 = Rs. 400. $$

Thus, the sum of money (principal) is **Rs. 400**, which corresponds to option **(a)**.

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