CBSE 2025 · Region 1 · Set 1 · Q32 · 5 marks
Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of $\displaystyle 8$% per annum and $\displaystyle 9$% per annum, respectively. He received ₹ $\displaystyle 1,860$ as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹ $\displaystyle 20$ more as annual interest. How much money did he invest in each scheme ?
Marking-scheme solution
Let Vijay invested ₹ x at $\displaystyle 8$% rate of interest & ₹ y at $\displaystyle 9$% rate of interestATQ,
\[\frac{8 \mathrm{x}}{100}+\frac{9 \mathrm{y}}{100}=1860
\]
or \(\displaystyle 8 \mathrm{x}+9 \mathrm{y}=186000 \quad \ldots \ldots\) (i)
\[\frac{9 \mathrm{x}}{100}+\frac{8 \mathrm{y}}{100}=1880
\]
or \(\displaystyle 9 \mathrm{x}+8 \mathrm{y}=188000 \quad \ldots \ldots\) (ii)On solving (i) and (ii), we get
\[\begin{aligned}
& x=12000 \\
& y=10000
\end{aligned}
\]
Hence, money invested in scheme A is ₹ $\displaystyle 12000$ and scheme B is ₹ 10000.
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