Profit and Loss Question 1 - CAT 2021
Raj invested ₹ 10000 in a fund. At the end of the first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two-year period is 35%, then the percentage of loss in the first year is:
Step-by-Step Explanation
Let the loss percentage in the first year be x%.
The growth percentage in the second year will be 5x%.
The overall gain over the two-year period is 35%, which means the final amount is:
Final Balance = 10000 × 1.35 = ₹ 13500
Set up the successive percentage tracking equation:
10000 × (1 − (x / 100)) × (1 + (5x / 100)) = 13500
(1 − (x / 100))(1 + (5x / 100)) = 1.35
Let x / 100 = z:
(1 − z)(1 + 5z) = 1.35
1 + 4z − 5z² = 1.35
5z² − 4z + 0.35 = 0
Multiply the entire equation by 20 to eliminate decimals:
100z² − 80z + 7 = 0
100z² − 70z − 10z + 7 = 0
10z(10z − 7) − 1(10z − 7) = 0
(10z − 1)(10z − 7) = 0
This yields two possible values for z:
z = 0.7 → x = 70%
z = 0.1 → x = 10%
The problem states that the balance at the end of the first year was more than ₹ 5000, meaning the first-year loss must be strictly less than 50%. Therefore, we discard 70%.
The loss percentage in the first year is 10%.
Correct Option: D
💡 FundaMakers Tip:
When the equation turns into a complex quadratic, stop and use the options to execute a quick back-calculation.
- Test Option D (10%): A 10% loss drops ₹ 10000 down to ₹ 9000.
- The second-year growth is 5 × 10% = 50%.
- Increasing ₹ 9000 by 50% yields 9000 + 4500 = ₹ 13500.
- Net gain = ₹ 3500, which is exactly 35% of the initial capital.
Verifying options takes less than 15 seconds and bypasses factorization completely.