A man donates 30% of his wealth to charity. Of the remaining amount, he gives 30% to his wife and 25% to his son. The remaining wealth is divided equally among his three daughters, and each daughter receives Rs 42 lakh. What was the man's total wealth (in lakh rupees)?

Introduction / Context:
This question deals with successive percentage allocations and then an equal division of the remaining amount. It combines percentage reduction and sharing problems, which are very common in aptitude sections that involve distribution of money among family members or partners. The key is to carefully track the remaining wealth after each stage.

Given Data / Assumptions:

• Total wealth of the man is W lakh rupees (unknown).
• He donates 30% of W to charity.
• From the remaining amount, he gives 30% to his wife.
• From the same remaining amount, he gives 25% to his son.
• The rest is equally divided among three daughters and each daughter gets Rs 42 lakh.

Concept / Approach:
We first determine what fraction of the original wealth remains after the donation to charity. Then we find how much of that remaining amount goes to the wife and son, and thus what fraction is left for the daughters. Once we have the fraction for the daughters, dividing it equally among three girls gives the share per daughter as a fraction of W. Since each daughter gets 42 lakh, we equate that fraction to 42 and solve for W. Percentages are converted into fractions to simplify the calculations.

Step-by-Step Solution:
Step 1: Let total wealth be W. Step 2: Donation to charity = 30% of W = 0.30W. Step 3: Wealth left after charity = W - 0.30W = 0.70W. Step 4: From this 0.70W, wife gets 30%: 0.30 * 0.70W = 0.21W. Step 5: From the same 0.70W, son gets 25%: 0.25 * 0.70W = 0.175W. Step 6: Total given to wife and son = 0.21W + 0.175W = 0.385W. Step 7: Wealth left for three daughters = 0.70W - 0.385W = 0.315W. Step 8: This 0.315W is divided equally among three daughters, so each daughter gets 0.315W / 3 = 0.105W. Step 9: Given that each daughter gets 42 lakh, so 0.105W = 42. Step 10: Therefore W = 42 / 0.105 = 400. Step 11: So the man's total wealth is 400 lakh rupees.

Verification / Alternative check:
Check using W = 400. Charity = 30% of 400 = 120, so remaining = 280. Wife gets 30% of 280 = 84. Son gets 25% of 280 = 70. Remaining for daughters = 280 - 84 - 70 = 126. Divided among three daughters, each gets 126 / 3 = 42. This matches the given share, so W = 400 is correct.

Why Other Options Are Wrong:

• 280: With this wealth, each daughter would get less than 42 lakh.
• 500: With 500 lakh, each daughter would get more than 42 lakh.
• 350 and 320: These values also fail to produce the required 42 lakh share when the same percentage distribution is applied.

Common Pitfalls:
Students sometimes incorrectly apply the percentages for the wife and son directly on the total W instead of on the remaining 0.70W, which changes all subsequent calculations. Another frequent error is to add the percentage amounts instead of properly subtracting them from the remaining wealth. Keeping track of each stage clearly and always noting the current base amount is essential for accuracy.

Final Answer:
The man's total wealth was 400 lakh rupees.