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 Rupees \(x\) be lent at 4% and the remaining Rupees \((2400-x)\) at 5%, both for 2 years.

Step 2: Total interest: \(\dfrac{x\times4\times2}{100}+\dfrac{(2400-x)\times5\times2}{100}=220\). Multiplying through by 50: \(4x+5(2400-x)=11000\).

Step 3: Expanding, \(4x+12000-5x=11000\), so \(-x=-1000\), giving \(x=1000\).

Step 4: The amount at 4% is Rupees 1000, and at 5% is \(2400-1000=1400\). \[ \boxed{Rupees\ 1000,\ Rupees\ 1400} \]