A and B invest in the ratio 4 : 5. After 3 months, A withdraws 1/4 of his capital and B withdraws 1/5 of his capital. If the total profit at the end of 10 months is ₹760, what is A's share?

Problem restatementCapitals change once during the year. Use time-weighted capitals to split the profit.

Given data

• Initial capitals: A = 4k, B = 5k.
• After 3 months: A withdraws 1/4 ⇒ new A = 3k; B withdraws 1/5 ⇒ new B = 4k.
• Total period = 10 months.

Concept/ApproachCompute capital-months before and after the change.

Step-by-step calculation First 3 months: A = 4k × 3 = 12k; B = 5k × 3 = 15k Next 7 months: A = 3k × 7 = 21k; B = 4k × 7 = 28k Totals: A = 12k + 21k = 33k; B = 15k + 28k = 43k Profit ratio A : B = 33 : 43 A's share = ₹760 × (33/(33+43)) = 760 × (33/76) = ₹330

Verification760 ÷ 76 = 10; 10 × 33 = ₹330 (A), remainder ₹430 (B). 330 : 430 = 33 : 43.

Common pitfalls

• Splitting by initial 4 : 5 ratio without time adjustments after withdrawals.

Final Answer₹330