Simple Interest and Compound Interest Question 2 - CAT 2022
Nitu has an initial capital of ₹ 20,000. Out of this, she invests ₹ 8,000 at 5.5% in bank A, ₹ 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:
Step-by-Step Explanation
- Analyze the total target interest:
The combined annual interest income is 5% of the initial capital of ₹ 20,000.
Total Target Interest = 5% of 20,000 = ₹ 1,000
- Calculate interest from Bank A and Bank B:
○ Bank A: ₹ 8,000 at 5.5% simple interest ⇒ 8,000 × 0.055 = ₹ 440
○ Bank B: ₹ 5,000 at 5.6% simple interest ⇒ 5,000 × 0.056 = ₹ 280
Combined Interest from A and B = 440 + 280 = ₹ 720
- Find the interest contribution from Bank C:
The remaining capital placed in Bank C is 20,000 − (8,000 + 5,000) = ₹ 7,000.
Interest needed from Bank C = 1,000 − 720 = ₹ 280
- Scale to find the hypothetical return:
The problem asks for the annual interest income if the entire initial capital (₹ 20,000) had been invested in bank C alone. We know that a principal of ₹ 7,000 yields ₹ 280 in Bank C. Because simple interest scales linearly with principal, we can set up a direct proportion:
New Interest = 280 / 7,000 × 20,000 = 4% of 20,000 = ₹ 800
Correct Option: B
💡 FundaMakers Tip:
Notice how we bypassed solving for the variable x entirely! Many students waste time calculating x = (280 x 100) / 7000 = 4% and then re-multiplying 4% by ₹ 20,000. In Simple Interest, returns scale proportionally with the principal. Recognizing that ₹ 280 comes from ₹ 7,000 allows you to directly scale it up to the ₹ 20,000 level using a single fraction, saving precious exam seconds.