Successive fraction-of-remaining spending with a rupee balance A man spends 1/7 of salary on food, half of the remaining on clothing, and 1/3 of the remaining on entertainment, and is left with Rs 600. How much did he spend on entertainment?

Introduction / Context:
This is a classic “fraction of the remainder” problem. Tracking successive expenditures as fractions of what remains at each stage and relating the final balance to the initial salary yields the entertainment amount.

Given Data / Assumptions:

• Salary = S (rupees).
• Food: spends 1/7 of S.
• Clothing: spends 1/2 of the remaining after food.
• Entertainment: spends 1/3 of the remaining after clothing.
• Final amount left = Rs 600.

Concept / Approach:
Work forward with remainders or backward from the final balance using inverse operations. Either way, express each stage in terms of S and solve.

Step-by-Step Solution:
After food: remaining = S − (1/7)S = (6/7)S.Clothing: spend (1/2) of remaining ⇒ (1/2)*(6/7)S = (3/7)S, leaving (6/7)S − (3/7)S = (3/7)S.Entertainment: spend (1/3) of remaining ⇒ (1/3)*(3/7)S = (1/7)S, leaving (3/7)S − (1/7)S = (2/7)S.Given leftover (2/7)S = 600 ⇒ S = 600 * (7/2) = 2100.Entertainment spend = (1/7)S = 2100/7 = Rs 300.

Verification / Alternative check:
Forward check: Food 300, remain 1800; Clothing 900, remain 900; Entertainment 300, remain 600 — consistent.

Why Other Options Are Wrong:
Rs 600 is the final balance, not the entertainment spend; Rs 450 and Rs 700 do not match the computed sequence; Rs 200 is inconsistent with the derived salary.

Common Pitfalls:
Applying fractions to the original salary instead of the remainder; mixing up “spend” vs. “left” amounts; arithmetic slips with sevenths.

Final Answer:
Rs. 300