If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit…

Partnership problems sometimes give capitals through an equality of multiples, such as k1 x A = k2 x B = k3 x C, instead of stating each partner's capital directly. In that case the capitals are inversely proportional to the given multipliers -- the capital ratio equals the ratio of the reciprocals of those multipliers, simplified to whole numbers using their LCM. Profit is then split in exactly the ratio of the capitals (assuming an equal investment period).

1. From 4(A) = 6(B) = 10(C), the capital ratio A : B : C is the ratio of the reciprocals: 1/4 : 1/6 : 1/10.

2. Multiplying each term by the LCM of 4, 6 and 10, which is 60, converts the ratio to whole numbers: 15 : 10 : 6.

3. Adding the parts gives 15 + 10 + 6 = 31 total parts.

4. Dividing the total profit of Rs. 4650 by 31 parts gives the value of one part: Rs. 4650 / 31 = Rs. 150.

5. C's share is 6 parts, so C receives 6 x Rs. 150 = Rs. 900.

As a check, multiplying the simplified ratio back by the original coefficients confirms equality: 4 x 15 = 60, 6 x 10 = 60, and 10 x 6 = 60 -- all equal, so the ratio 15 : 10 : 6 is correct. Also, 15x150 + 10x150 + 6x150 = 2250 + 1500 + 900 = 4650, matching the given total profit.