Question

Veeru gave Rupees 2400 on loan. Some amount he gave at 4\% per annum simple interest and remaining at 5\% per annum simple interest. After two years he got Rupees 220 as interest. Then the amount given at 4\% and 5\% per annum simple interest are, respectively?

• A. Rupees 1000, Rupees 1400
• B. Rupees 800, Rupees 1600
• C. Rupees 1800, Rupees 600
• D. Rupees 2200, Rupees 200

Hint:

For such problems, assign one variable and use SI = \( \frac{PRT}{100}\). Remember total principal = sum of parts, and total interest = sum of interests.

Answer 1

The Correct Option is A

Step 1: Let the amounts be variables.
Suppose \(\,x\) at 4\% and \((2400-x)\) at 5\%. Step 2: Write simple interest equations.
Simple interest formula: \(SI = \frac{P \cdot R \cdot T}{100}\). For 2 years: Interest on \(x\): \( \frac{x \cdot 4 \cdot 2}{100} = \frac{8x}{100} = \frac{2x}{25}\).
Interest on \((2400-x)\): \( \frac{(2400-x)\cdot 5\cdot 2}{100} = \frac{10(2400-x)}{100} = \frac{2400-x}{10}\). Step 3: Form the equation.
\[ \frac{2x}{25} + \frac{2400-x}{10} = 220 \] Multiply through by 50: \[ 4x + 5(2400-x) = 11000 \] \[ 4x + 12000 - 5x = 11000 \] \[ - x + 12000 = 11000 \quad \Rightarrow \quad x = 1000 \] So, at 4\%: Rupees 1000; at 5\%: \(2400-1000=1400\). \[ \boxed{1000,\ 1400} \]