A man spends 7.5% of his money first, and then spends 75% of the remaining amount. After these two expenditures he is left with Rs 370. How much money did he originally have?

Introduction / Context:
This question involves successive percentage reductions of a total amount of money. It is typical of percentage and income expenditure questions, where part of the money is spent in stages and the final remaining balance is known. The task is to work backwards to find the original amount before any spending took place.

Given Data / Assumptions:

• The person initially has an unknown amount of money, say M.
• He spends 7.5% of M first.
• He then spends 75% of the remaining amount after the first spending.
• He is left with Rs 370 after both spendings.

Concept / Approach:
We treat each spending as a percentage reduction applied successively. After spending 7.5% of M, he retains 92.5% of M. Then he spends 75% of that remaining amount, so he retains only 25% of the remaining amount. Overall, the final money left is a certain fraction of the original M. Once we express that fraction, we equate it to Rs 370 and solve for M using simple algebra. This is a good example of how successive percentage changes multiply rather than add.

Step-by-Step Solution:
Step 1: Let the original money be M. Step 2: First spending = 7.5% of M = 0.075 * M. Step 3: Money left after first spending = M - 0.075M = 0.925M. Step 4: Second spending = 75% of 0.925M = 0.75 * 0.925M = 0.69375M. Step 5: Money left after second spending = 0.925M - 0.69375M = 0.23125M. Step 6: According to the question, 0.23125M = 370. Step 7: So M = 370 / 0.23125 = 1600. Step 8: Therefore, the man originally had Rs 1600.

Verification / Alternative check:
We can check by forward calculation. Start with M = 1600. First spending = 7.5% of 1600 = 0.075 * 1600 = 120. Remaining = 1600 - 120 = 1480. Second spending = 75% of 1480 = 0.75 * 1480 = 1110. Remaining = 1480 - 1110 = 370. This matches the given remaining amount, so the calculation is correct.

Why Other Options Are Wrong:

• 1200: If M were 1200, the final remainder after the same steps would not be 370 but a smaller amount.
• 1500: This would also result in a different remaining amount after two spendings.
• 1400: Applying the same process to 1400 does not end with 370.
• 1800: With 1800, the remaining balance after both reductions would be higher than 370.

Common Pitfalls:
Students sometimes subtract percentages incorrectly by adding 7.5% and 75% as if the man spent 82.5% of his money in one shot. That ignores the fact that 75% is taken from the remaining amount, not from the original. Another common mistake is to forget to convert percentages into decimals before multiplication. Writing each step with clear fractional or decimal values helps avoid these errors.

Final Answer:
The man originally had Rs 1600 before he started spending.