Question
'A' and 'S' ventured into a business with initial investments of Rs. "w + 32" and Rs.'w', respectively. After 'x' months, 'V' joined them with an initial investment that was 20% greater than 'A's initial investment. At the conclusion of '2x' months, the ratio of profit shares for A, S, and V was 6x:14y:9z, respectively. Determine which of the following relation(s) holds true in this scenario.
I. z = 0.4x
II. w = 448y/[15z – 14y]
III. w = 224y/[3x – 7y]
Solution
ATQ, Ratio of profit share of A, S and V = [(w + 32) × 2x]:[w × 2x]:[1.2 × (w + 32) × x] So, [(w + 32) × 2x]/[1.2 × (w + 32) × x] = 6x/9z So, (2/1.2) = (2x/3z) So, z = (1.2x/3) = 0.4x And, [w × 2x]:[1.2 × (w + 32) × x] = (14y/9z) So, w/[0.6 × (w + 32)] = 14y/9z Or, w = 448y/[15z – 14y] And, [(w + 32) × 2x]:[w × 2x] = 6x/14y = 3x/7y Or, w = 224y/[3x – 7y]
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