Question

Mr. Dua invested money in two schemes, A and B offering compound interest @ 8 p.c.p.a and 12 p.c.p.a respectively. If the total amount of interest accrued through two schemes together in two years was Rs.\ 4538.00 and the total amount invested was Rs.\ 20,000, what was the amount invested in Scheme A?

• A. Rs.\ 6000
• B. Rs.\ 6250
• C. Rs.\ 6500
• D. Rs.\ 16000
• E. Rs.\ 16500

Answer 1

The Correct Option is B

Concept: Compound interest for 2 years: \[ \text{CI} = P\left[\left(1+\frac{r}{100}\right)^2 - 1\right] \]
Step 1: Let investment in A = \(x\).
\[ \text{Investment in B} = 20000 - x \]
Step 2: CI formulas.
For A (8%): \[ x\left[(1.08)^2 - 1\right] = x(1.1664 - 1) = 0.1664x \] For B (12%): \[ (20000-x)\left[(1.12)^2 - 1\right] = (20000-x)(1.2544 -1) = 0.2544(20000-x) \]
Step 3: Total interest.
\[ 0.1664x + 0.2544(20000 - x) = 4538 \]
Step 4: Solve.
\[ 0.1664x + 5088 - 0.2544x = 4538 \] \[ -0.088x = -550 \Rightarrow x = 6250 \]
Step 5: Option analysis.

• (A) Incorrect $\times$
• (B) Correct \checkmark
• (C) Incorrect $\times$
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).