Mr. Dua invested money in two schemes A and B | vedclass

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Question

(A) Let the amount invested in scheme $A$ be $₹ x$. Then,the amount invested in scheme $B$ is $₹ (27000 - x)$. Compound interest for $2$ years is give

Vedclass · Accepted Answer

$12000$

Vedclass · Answer

(A) Let the amount invested in scheme $A$ be $₹ x$. Then,the amount invested in scheme $B$ is $₹ (27000 - x)$. Compound interest for $2$ years is given by the formula $P[(1 + r/100)^n - 1]$. For scheme $A$: $CI_A = x[(1 + 8/100)^2 - 1] = x[(1.08)^2 - 1] = x[1.1664 - 1] = 0.1664x$. For scheme $B$: $CI_B = (27000 - x)[(1 + 9/100)^2 - 1] = (27000 - x)[(1.09)^2 - 1] = (27000 - x)[1.1881 - 1] = 0.1881(27000 - x)$. The total interest is $4818.30$. So,$0.1664x + 0.1881(27000 - x) = 4818.30$. $0.1664x + 5078.7 - 0.1881x = 4818.30$. $-0.0217x = 4818.30 - 5078.7$. $-0.0217x = -260.4$. $x = 260.4 / 0.0217 = 12000$. Thus,the amount invested in scheme $A$ is ₹ $12000$.

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