Three partners invest in an AI analytics firm in the ratio 8 : 11 : 13. After 6 months, the second partner increases his investment by 25%, while the first partner reduces his investment by 20%. If the total profit after 12 months is ₹9,24,000, then what is the share of the third partner (in ₹, rounded off to the nearest integer)?
3,68,749
Profit is shared in the ratio of capital × time. Take the initial investments as 8, 11 and 13 units.
First partner: 8 for 6 months and 8 × 0.8 = 6.4 for 6 months, so 48 + 38.4 = 86.4. Second partner: 11 for 6 months and 11 × 1.25 = 13.75 for 6 months, so 66 + 82.5 = 148.5. Third partner: 13 × 12 = 156.
Ratio of shares = 86.4 : 148.5 : 156, total = 390.9.
Share of the third partner = \(\frac{156}{390.9} \times 924000 \approx 368749.04\), which rounds to ₹3,68,749.
Check: the other shares are \(\frac{86.4}{390.9} \times 924000 \approx 204230.24\) and \(\frac{148.5}{390.9} \times 924000 \approx 351020.722\); 204230.24 + 351020.722 + 368749.04 ≈ 924000, so the shares add up to the total profit.
Hence, 3,68,749.
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