David invested in three schemes A, B, C at $10\%$, $12\%$, $15\%$ p.a. respectively. The total interest in one year was ₹3200. Also, $C$ was $150\%$ of $A$ and $240\%$ of $B$. What was the amount invested in $B$?
David invested in three schemes A, B, C at $10\%$, $12\%$, $15\%$ p.a. respectively. The total interest in one year was ₹3200. Also, $C$ was $150\%$ of $A$ and $240\%$ of $B$. What was the amount invested in $B$?
Show Hint
₹5000
₹6500
₹8000
cannot be determined
The Correct Option is A
Solution and Explanation
Let amounts be $A=a,\;B=b,\;C=c$. Given $c=1.5a$ and $c=2.4b\Rightarrow b=\frac{c}{2.4}=0.625a$.
Interest eqn: $0.10a+0.12b+0.15c=3200$. Substitute $b,c$: \[ 0.10a+0.12(0.625a)+0.15(1.5a)= (0.10+0.075+0.225)a=0.40a=3200 \Rightarrow a=8000. \] Hence $b = 0.625a = 0.625 \times 8000 = \boxed{\text{₹}\,5000}$.
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