# CAT 2022 Set-3 | Quantitative Aptitude | Question: 10

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Nitu has an initial capital of ₹ $20,000$. Out of this, she invests ₹$8,000$ at $5.5 \%$ in bank $\mathrm{A}$, ₹$5,000$ at $5.6 \%$ in bank $\mathrm{B}$ and the remaining amount at $x \%$ in bank $\mathrm{C}$, each rate being simple interest per annum. Her combined annual interest income from these investments is equal to $5 \%$ of the initial capital. If she had invested her entire initial capital in bank $\mathrm{C}$ alone, then her annual interest income, in rupees, would have been

1. $900$
2. $800$
3. $1000$
4. $700$

Total Capital is 20000. Invested 8000 @5.5% per annum in bank A, 5000 @5.6% per annum in bank B, and remaining i.e., 7000(20k-8k-5k) @x% per annum in bank C.

And the combined annual interest income from these investments is equal to 5% of the initial capital (20k).

So, the equation is (8000 * 5.5 * 1)/100 + (5000 * 5.6 * 1)/100 + (7000 * x * 1)/100 = (20000 * 5 * 1)/100

=>  440 + 280 + 70x = 1000  => x = 4

If she had invested her entire initial capital in bank C alone, then her annual interest income, in rupees, would have been (20000 x 4 x 1)/100 = 800. Ans is B.

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