Let the principal sum be denoted by P.

Simple Interest Calculations

The formula for Simple Interest (SI) is given by: $ SI = \frac{P \times R \times T}{100} $ Where P = Principal, R = Rate of Interest per annum, T = Time period in years.

Scenario 1

• Time ($T_1$) = $3\frac{1}{2}$ years = $3.5$ years
• Rate ($R_1$) = $12\%$ per annum
• Simple Interest ($SI_1$) = $ \frac{P \times 12 \times 3.5}{100} $
• $SI_1 = \frac{42P}{100}$

Scenario 2

• Time ($T_2$) = $4\frac{1}{2}$ years = $4.5$ years
• Rate ($R_2$) = $10\%$ per annum
• Simple Interest ($SI_2$) = $ \frac{P \times 10 \times 4.5}{100} $
• $SI_2 = \frac{45P}{100}$

Finding the Principal Sum

According to the question, the simple interest in the first scenario is ₹ 60 less than the simple interest in the second scenario. $ SI_1 = SI_2 - 60 $ Rearranging the equation: $ SI_2 - SI_1 = 60 $

Substitute the expressions for $SI_1$ and $SI_2$: $ \frac{45P}{100} - \frac{42P}{100} = 60 $

Combine the terms on the left side: $ \frac{45P - 42P}{100} = 60 $ $ \frac{3P}{100} = 60 $

Solve for P: $ 3P = 60 \times 100 $ $ 3P = 6000 $ $ P = \frac{6000}{3} $ $ P = 2000 $

Therefore, the sum (principal) is ₹ 2000.