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: \(SI = \dfrac{P \cdot R \cdot T}{100}\). For 2 years: Interest on \(x\): \( \dfrac{x \cdot 4 \cdot 2}{100} = \dfrac{8x}{100} = \dfrac{2x}{25}\). 

Interest on \((2400-x)\): \( \dfrac{(2400-x)\cdot 5\cdot 2}{100} = \dfrac{10(2400-x)}{100} = \dfrac{2400-x}{10}\). 

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%: \(2400-1000=1400\). \[ \boxed{1000,\ 1400} \]