A, B and C enter into a partnership. Their capital contribution

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A, B and C enter into a partnership. Their capital contribution is in the ratio 21 : 18 : 14. At the end of the business term they share profits in the ratio 15 : 8 : 9. Find the ratio of time for which they invest their capitals

1. 37 : 38 : 72
2. 39 : 38 : 72
3. 90 : 56 : 81
4. None of these

Correct Option: C

Here , Ratio of their capital = 4 : 8 : 9
Ratio of their share profits = 15 : 8 : 9
Ratio of profits = (Ratio of capital by time).
∴ Ratio of time = Ratio of profit divided by respective capitals.

Ratio of time =		15	:	8	:	9
		21		18		14

Ratio of time =		5	:	4	:	9
		7		9		14

Ratio of time =		90	:	56	:	81	[126 is LCM of 7, 9 and 14]
		126		126		126

Hence , Ratio of time of A , B and C = 90 : 56 : 81.