A lends ₹ 2500 to B and a certain sum to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives ₹ 1120 as interest from B and C, then the sum lent to C is :

### Concept & Additive Simple Interest When a total interest amount is given from multiple sources, it is the sum of the individual simple interests calculated separately using: $$SI = \frac{P \times R \times T}{100}$$ Total $SI$ = $SI_1 + SI_2$ ### Step-by-Step Solution * **Given:** * For B: $P_1 = 2500$, $R = 7\%$, $T = 4$ years. * For C: $P_2 = x$, $R = 7\%$, $T = 4$ years. * Total Interest = $1120$. * **Calculation:** Express the total interest as an equation: * $1120 = \left(\frac{2500 \times 7 \times 4}{100}\right) + \left(\frac{x \times 7 \times 4}{100}\right)$ * Simplify the terms: * $1120 = (25 \times 28) + \left(\frac{28x}{100}\right)$ * $1120 = 700 + 0.28x$ * Subtract 700 from both sides: * $420 = 0.28x$ * Solve for $x$: * $x = \frac{420}{0.28} = \frac{42000}{28} = 1500$. ### Exam Strategy & Shortcut Instead of calculating separate interests, calculate the combined principal since rate and time are identical for both. Total Interest = $\frac{\text{Total Principal} \times R \times T}{100}$ $1120 = \frac{(2500 + x) \times 7 \times 4}{100}$ $1120 = (2500 + x) \times \frac{28}{100}$ $2500 + x = 1120 \times \frac{100}{28} = 40 \times 100 = 4000$. $x = 4000 - 2500 = 1500$. ### Common Pitfall A common error is confusing the total interest received with the total amount received. The problem specifies ₹ 1120 is the *interest*. ### Final Answer Therefore, the correct answer is **₹ 1500**.