Mr. Shankar spends 25% of his monthly salary on household expenditure, 20% of the remaining on children education, and invests the entire balance equally in three different schemes. If the amount invested in each scheme is Rs. 5,600, what is his monthly salary?

Introduction / Context:
This is a percentage and allocation problem involving a person's monthly salary distributed across expenses and investments. After a sequence of percentage deductions, the remaining amount is invested equally into three schemes. From the amount invested in each scheme, we must reverse the steps to compute the original monthly salary of Mr. Shankar.

Given Data / Assumptions:

• Shankar spends 25% of his monthly salary on household expenses.
• He spends 20% of the remaining amount on children education.
• The rest is invested equally in three schemes.
• Amount invested in each scheme = Rs. 5,600.
• There are exactly three schemes, so the total invested amount is 3 * 5,600.

Concept / Approach:
Let the monthly salary be S. We apply the percentage expenditures stepwise and express the final balance (which is invested) in terms of S. Since we know the amount invested in each scheme, we equate the total investment with the final balance and solve for S. The idea is to work from the end (invested amount) back to the beginning (salary).

Step-by-Step Solution:
Step 1: Let monthly salary = S rupees. Step 2: Shankar spends 25% of S on household expenditure, so household spending = 0.25 * S. Step 3: Amount left after household expenses = S - 0.25 * S = 0.75 * S. Step 4: He spends 20% of this remaining amount on children education: 0.20 * 0.75 * S = 0.15 * S. Step 5: Amount left after children education = 0.75 * S - 0.15 * S = 0.60 * S. Step 6: This remaining 60% of S is invested equally in three schemes. Step 7: Amount invested in each scheme = Rs. 5,600, so total invested = 3 * 5,600 = Rs. 16,800. Step 8: Therefore, 0.60 * S = 16,800. Step 9: Solve for S: S = 16,800 / 0.60 = 28,000. Step 10: Hence, Shankar's monthly salary is Rs. 28,000.

Verification / Alternative check:
Check the distribution using S = 28,000. Household expenditure = 25% of 28,000 = 7,000. Remaining = 21,000. Children education = 20% of 21,000 = 4,200. Remaining = 16,800. This remaining amount is invested, and divided equally into three schemes each receives 16,800 / 3 = 5,600. Everything is consistent with the problem statement.

Why Other Options Are Wrong:
For Rs. 34,000 or Rs. 31,245, the final remaining amount after the given percentage deductions would not equal Rs. 16,800, and the per-scheme investment would differ from Rs. 5,600. Rs. 24,315 and Rs. 30,000 similarly fail to reproduce the given invested amount per scheme. Only Rs. 28,000 leads to a final investable amount of Rs. 16,800, matching all conditions.

Common Pitfalls:
Students often mix up the base for each percentage, incorrectly applying 20% to the original salary instead of to the remaining amount. Another common mistake is to treat the 60% remaining as 55% by subtracting 25% and 20% directly. Here the second percentage applies to the remaining money, not to the whole salary, so the final fraction is 0.75 * 0.80 = 0.60 of S.

Final Answer:
The monthly salary of Shankar is Rs. 28,000.