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CAT 2022 Slot 3 — QA Question 20

Simple InterestEasy

Nitu has an initial capital of Rs. 20,000. Out of this, she invests Rs. 8,000 at 5.5% in bank A, Rs. 5,000 at 5.6% in bank B and the remaining amount at x% in bank 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 C alone, then her annual interest income, in rupees, would have been
 

Answer & solution

  • 800

  • B

    700

  • C

    900

  • D

    1000

Solution

Easy

Total interest equals 5%5\% of the capital. Set up one equation for the unknown rate x%x\% in bank C, solve for xx, then compute the interest had the whole capital gone into bank C.

1

Interest from each bank. Remaining in C =20000−8000−5000=7000=20000-8000-5000=7000:

A:8000×5.5%=440B:5000×5.6%=280C:7000×x%=70x\begin{aligned} &A:8000\times 5.5\%=440\\ &B:5000\times 5.6\%=280\\ &C:7000\times x\%=70x \end{aligned}
2

Total = 5%5\% of 20000=100020000=1000. Solve for xx:

440+280+70x=100070x=280 ⇒ x=4\begin{aligned} &440+280+70x=1000\\ &70x=280\ \Rightarrow\ x=4 \end{aligned}
3

Entire capital in bank C at 4%4\%:

20000×4%=80020000\times 4\%=800

Her annual interest income would be Rs. 800\mathbf{Rs.\ 800}.

CAT 2022 Slot 3 QA Q20: Nitu has an initial capital of Rs. 20,000. Out of this, she invests Rs. 8,000 at 5.5% in bank A, Rs. 5,000 at — Solution | TheCATExam