Question

Archit 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. 3508, then determine the amount invested in Scheme B by Archit?

• A. Rs. 6400
• B. Rs. 6500
• C. Rs. 7200
• D. Rs. 7500
• E. Rs. 6800

Hint:

For questions splitting an investment across two rates, you can also use the method of Alligation by calculating the overall average interest rate for the combined sum.

Answer 1

The Correct Option is A

Step 1: Calculate simple interest for 1 year.
Total SI for 2 years = 3508.
Total SI for 1 year = $\frac{3508}{2} = 1754$.

Step 2: Set up the algebraic equations.
Let the investment in Scheme A be $x$ and in Scheme B be $y$.
Equation 1: $x + y = 13900$
Equation 2: $0.14x + 0.11y = 1754$

Step 3: Solve for $y$ (Scheme B).
Multiply Equation 1 by 0.14: $0.14x + 0.14y = 1946$.
Subtract Equation 2 from this new equation:
$(0.14x + 0.14y) - (0.14x + 0.11y) = 1946 - 1754$
$0.03y = 192$
$y = \frac{192}{0.03} = 6400$.