Question

Susan invested certain amount of money in two schemes $A$ and $B$, which offer interest at the rate of $8\%$ per annum and $9\%$ per annum, respectively. She received Rs. $1860$ as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs. $20$ more as annual interest. How much money did she invest in each scheme?

• A. Rs. $13000$ in scheme $A$, Rs. $12000$ in scheme $B$
• B. Rs. $12000$ in scheme $A$, Rs. $10000$ in scheme $B$
• C. Rs. $11000$ in scheme $A$, Rs. $10000$ in scheme $B$
• D. Rs. $10000$ in scheme $A$, Rs. $13000$ in scheme $B$

Answer 1

Answer: (B)

Rs. $12000$ in scheme $A$, Rs. $10000$ in scheme $B$

Let amount invested in $A$ be Rs. $x$ and in $B$ be Rs. $y$.
As per the given statements, $0.08x+0.09y=1860$.....$\left(1\right)$
And, $0.09x+0.08y=1880$.....$\left(2\right)$

Multiplying equation $\left(1\right)$ with $8$ we get, $0.64x+0.72y=14880$.....$\left(3\right)$

Multiplying equation $\left(2\right)$ with $9$ we get, $0.81x+0.72y=16920$.....$\left(4\right)$

Subtracting equation $\left(3\right)$ from $\left(4\right)$, we get $0.17x=2040=>x=12000$
Substituting $x=12000$ in the equation $\left(1\right)$, we get $0.08\left(12000\right)+0.09y=1860\Rightarrow y=10000$

Hence, amount invested $A$ is Rs. $12000$ and in $B$ is Rs. $10000$