Simple Interest and Compound Interest Question 3 - CAT 2024
An amount of Rs. 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is:
Simple Interest and Compound Interest Shortcuts & Tricks
Let the investment period in bank A be x years.
- Bank A Interest (Iₐ):
Principal = Rs. 10000, Rate = 5% simple interest.
Iₐ = 10000 × 0.05 × x = 500x
Maturity Amount from Bank A = 10000 + 500x
- Bank B Interest (Iᵦ):
The entire maturity amount from Bank A is deposited for 5 years at 6% simple interest.
Iᵦ = (10000 + 500x) × 0.06 × 5
Iᵦ = (10000 + 500x) × 0.30 = 3000 + 150x
- Use the interest ratio:
The ratio of interest earned from bank A to bank B is 10 : 13:
500x / (3000 + 150x) = 10 / 13
Simplify the fraction by dividing the numerator and denominator on the left by 50:
10x / (60 + 3x) = 10 / 13
Cancel out 10 from both numerators:
x / (60 + 3x) = 1 / 13
13x = 60 + 3x
10x = 60 ⇒ x = 6
The investment period in bank A was 6 years.
Correct Option: D
💡 FundaMakers Tip:
Reduce the trailing zeros early on to minimize calculation clutter. Instead of carrying around Rs. 10,000, assume the principal is 100 units.
- Interest from A = 5x units.
- New Principal for B = 100 + 5x.
- Interest from B = (100 + 5x) × 30% = 30 + 1.5x.
Equating 5x / (30 + 1.5x) = 10 / 13 yields x = 6 seamlessly. Keeping the numbers small prevents simple zero-tracking oversights.