Aman invests ₹70,000 from the start. Rakhi joins after 6 months with ₹1,05,000, and Sagar joins 6 months later with ₹1,40,000. If the profit is distributed 3 years after Aman started, in what ratio should Aman : Rakhi : Sagar share the profit?

Problem restatement
Profits in partnerships are divided in proportion to capital × time. We are given different joining times over a total horizon of 3 years (36 months).

Given data

• Aman: ₹70,000 invested for 36 months.
• Rakhi: ₹1,05,000 invested for 30 months (joins after 6 months).
• Sagar: ₹1,40,000 invested for 24 months (joins after another 6 months).

Concept/Approach
Profit shares are proportional to the product of amount invested and duration invested.

Step-by-step calculation
Aman's units = 70,000 × 36 = 25,20,000 Rakhi's units = 1,05,000 × 30 = 31,50,000 Sagar's units = 1,40,000 × 24 = 33,60,000 Divide all by 10,000 → 252 : 315 : 336 Simplify by 21 → 12 : 15 : 16

Verification/Alternative
Check months: 36, 30, 24 correctly reflect 0, 6, 12-month join points across 36-month horizon.

Common pitfalls

• Using only capital ratios and ignoring time weighting.
• Using 12 and 18 months for later partners (misreading the 6-month gaps).

Final Answer
12 : 15 : 16