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Q.

Three partners shared the profit in business in the ratio $5 : 7 : 8$ . They had partnered for 14 months, 8 months, 7 months respectively. What was the ratio of their investments?

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a

$28 : 49 : 64$

b

$21 : 28 : 38$

c

$5 : 7 : 8$

d

$38 : 28 : 21$

answer is A.

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Detailed Solution

$\begin{array}{l} 14 x : 8 y : 7 z = 5 : 7 : 8 \\ \frac{14 x}{8 y} = \frac{5}{7} \Rightarrow 70 x = 40 y \Leftrightarrow y = \frac{7}{4} x \\ \Leftrightarrow z = \frac{112}{35} x \Rightarrow x = \frac{16}{5} x \\ ∴ x : y : z = x = \frac{7}{4} x = \frac{16}{5} x \Rightarrow 20 : 35 : 64 \end{array}$

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Three partners shared the profit in business in the ratio 5:7:8. They had partnered for 14 months, 8 months, 7 months respectively. What was the ratio of their investments?