Question

Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of \(14%\) p.a. and \(11%\) p.a. respectively. If the total amount of simple interest earned in 2 years is Rs. 3,508, what was the amount invested in Scheme B?

• A. Rs. 6400
• B. Rs. 6500
• C. Rs. 7200
• D. Rs. 7500

Hint:

When dealing with two-part investments, form one equation using the total interest and solve systematically. Always recheck by calculating each part's interest separately.

Answer 1

The Correct Option is C

Step 1 (Assign variables).
Let the amount invested in Scheme A be \(x\) and in Scheme B be \(13900 - x\). Step 2 (Calculate interest from each scheme).
Interest from Scheme A for 2 years: \[ \text{SI}_A = \frac{x \times 14 \times 2}{100} = 0.28x \] Interest from Scheme B for 2 years: \[ \text{SI}_B = \frac{(13900 - x) \times 11 \times 2}{100} = 0.22(13900 - x) \] Step 3 (Total interest equation).
Total simple interest from both schemes is given as Rs. 3,508: \[ 0.28x + 0.22(13900 - x) = 3508 \] Step 4 (Simplify).
\[ 0.28x + 3058 - 0.22x = 3508 \] \[ 0.06x + 3058 = 3508 \] \[ 0.06x = 450 \] \[ x = \frac{450}{0.06} = 7500 \] Step 5 (Find Scheme B amount).
\[ \text{Amount in B} = 13900 - 7500 = 6400 \] Step 6 (Recheck).
Interest from A: \( \frac{7500 \times 14 \times 2}{100} = 2100\)
Interest from B: \( \frac{6400 \times 11 \times 2}{100} = 1408\)
Total interest \(= 2100 + 1408 = 3508\) So the correct amount invested in Scheme B is Rs. 6400. \[ \boxed{6400 \ \text{rupees (Option (a)}} \]