David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was ` 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B ?
(a)` 5000
(b)` 6500
(c)` 8000
(d)Cannot be determined
(e)None of these
Answer
Answer (as printed): A
Explanation
Let $x, y$ and $z$ be the amounts invested in schemes A, B and C respectively. Then, $\left(\frac{x \times 10 \times 1}{100}\right)+\left(\frac{y \times 12 \times 1}{100}\right)+\left(\frac{z \times 15 \times 1}{100}\right)=3200 \Leftrightarrow 10 x+12 y+15 z=320000$ ... (i) Now, $z=240\%$ of $y=\frac{12}{5} y$ ... (ii) And, $z=150\%$ of $x=\frac{3}{2} x \Rightarrow x=\frac{2}{3} z=\frac{2}{3}\times\frac{12}{5} y=\frac{8}{5} y$ ... (iii) From (i), (ii) and (iii), we have: $16y+12y+36y=320000 \Leftrightarrow 64y=320000 \Leftrightarrow y=5000$. ∴ Sum invested in Scheme B = ₹5000.
Explanation as extracted from the printed page; notation may be imperfect.