'A', 'B', and 'C' formed a consulting firm. Their capital investments were Rs. 6,00,000, Rs. 4,00,000, and Rs. 5,00,000, respectively. After 3 months, 'A' withdrew Rs. 1,00,000, and 'B' added Rs. 1,00,000. The partnership lasted for 9 months. What was the ratio of their effective capital contributions?
16:14:15
In partnership, the effective contribution of each partner is the sum of (capital invested) \(\times\) (number of months it stayed invested). Working in units of Rs. 1,00,000 over 9 months:
'A' kept Rs. 6,00,000 for the first 3 months, then withdrew Rs. 1,00,000, leaving Rs. 5,00,000 for the remaining 6 months: \(6\times3 + 5\times6 = 18 + 30 = 48\).
'B' kept Rs. 4,00,000 for the first 3 months, then added Rs. 1,00,000, making Rs. 5,00,000 for the remaining 6 months: \(4\times3 + 5\times6 = 12 + 30 = 42\).
'C' kept Rs. 5,00,000 unchanged for all 9 months: \(5\times9 = 45\).
So the ratio of effective contributions is \(48:42:45\). Dividing each term by 3 gives \(16:14:15\).
Hence, the ratio of their effective capital contributions is 16:14:15.
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