A sum of money lent out at simple interest amounts to ₹ 720 after 2 years and to ₹ 1020 after a further period of 5 years. The sum is (S.S.C., 2004)

### Concept & Simple Interest The difference in the amounts over a certain period gives the simple interest for that specific duration. $$Simple Interest = \frac{Principal \times Rate \times Time}{100}$$ ### Step-by-Step Solution * The problem states the amount is ₹ 1020 after a "further period of 5 years". This means the total time is $2 + 5 = 7$ years. * Amount in 7 years = ₹ 1020 * Amount in 2 years = ₹ 720 * S.I. for 5 years (which is $7 - 2$) = ₹ 1020 - ₹ 720 = ₹ 300 * S.I. for 1 year = $\frac{300}{5}$ = ₹ 60 * S.I. for 2 years = ₹ 60 × 2 = ₹ 120 * Principal = Amount in 2 years - S.I. for 2 years = ₹ 720 - ₹ 120 = ₹ 600 ### Exam Strategy & Shortcut Recognize "further period" means the interest earned in those specific 5 years is $1020 - 720 = 300$. So, yearly interest is $60$. Subtract 2 years of interest ($120$) from the 2-year amount ($720$) to get $600$. ### Common Pitfall Assuming ₹ 1020 is the amount after 5 years total, rather than after a *further* 5 years (7 years total). ### Final Answer Therefore, the correct answer is **₹ 600**.