Rohan spends 24% of his money on an insurance policy, 34% on food, 19% on children education and 17% on recreation; the remaining Rs. 540 is deposited in a bank; what total amount does he spend on food and his insurance policy together?

Introduction / Context:
This problem is similar in structure to many household budget questions where a person divides income into several percentage based heads and saves the rest. We are told the exact amount saved and some spending percentages. The key skill is reversing percentage operations to recover the total income and then calculating how much is spent on particular categories, here food and insurance policy.

Given Data / Assumptions:

• Rohan spends 24% on an insurance policy.
• He spends 34% on food.
• He spends 19% on children education.
• He spends 17% on recreation.
• The remaining amount deposited in a bank is Rs. 540.
• We have to find the combined amount spent on food and insurance policy.

Concept / Approach:
The total percentage spent on the four listed heads is first computed. Whatever remains out of 100% is the percentage that corresponds to the known bank deposit. Once we know that this remaining percentage equals Rs. 540, we find the whole amount using a simple proportion. After recovering the total money, we calculate the combined spending on food and insurance as a fixed percentage of that total. This forward and backward movement between percentages and absolute values is standard in percentage applications.

Step-by-Step Solution:
Total percentage spent on all given heads = 24% + 34% + 19% + 17% = 94%.Therefore remaining percentage for bank deposit = 100% - 94% = 6%.Given that 6% of Rohan total money equals Rs. 540.Let total money be T rupees. Then 0.06 * T = 540.So T = 540 / 0.06 = 9000 rupees.Combined percentage for food and insurance policy = 34% + 24% = 58%.Amount spent on food and insurance = 0.58 * 9000 = 5220 rupees.

Verification / Alternative check:
We can verify by reconstructing the entire budget using T = 9000. Insurance policy: 24% of 9000 is 2160. Food: 34% of 9000 is 3060. Education: 19% of 9000 is 1710. Recreation: 17% of 9000 is 1530. Total expenses = 2160 + 3060 + 1710 + 1530 = 8460. Remaining amount is 9000 - 8460 = 540, exactly matching the given bank deposit. Also, the combined amount for insurance and food is 2160 + 3060 = 5220, confirming the result.

Why Other Options Are Wrong:
Rs. 6350, Rs. 5890 and Rs. 6458 all exceed 58% of 9000 and would leave negative or inconsistent balances when other heads and savings are included.

Any of these values would not allow a remaining amount of exactly Rs. 540, so they cannot satisfy all given conditions simultaneously.

Common Pitfalls:
Some students mistakenly treat Rs. 540 as a part of the spending rather than the leftover savings and compute 94% of some unknown amount as 540. Others add the food and insurance percentages incorrectly or forget to divide by 0.06 correctly. Carefully writing down the formula for the remaining percentage and verifying total allocations at the end is a good practice to avoid these errors.

Final Answer:
The total amount Rohan spends on food and insurance policy together is Rs. 5220.