Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
A. 5 : 7 : 8 B. 20 : 49 : 64 C. 38 : 28 : 21 D. None of these Answer: Option BShow Answer
Solution(By Apex Team)
$\begin{array}{l}\text{Let their investments be}\\
\text{Rs. x for 14 months,}\\
\text{Rs. y for 8 months and}\\
\text{Rs. z for 7 months respectively.}\\
\text{Then,}\\
14x\ :\ 8y\ :\ 7z\\
=5\ :\ 7\ :\ 8\end{array}$
$\begin{aligned}\text{ Now },\frac{14x}{8y}=\frac{5}{7}&\\
98x&=40y\\
y=&\frac{49}{20}x\\
\text{ And, }\frac{14x}{7z}=\frac{5}{8}&\\
112x=35z&\\
&z=\frac{112}{35}x=\frac{16}{5}x\\
&\therefore x:y:z\\
=&x:\frac{49}{20}x:\frac{16}{5}x\\
=&20:49:64\end{aligned}$
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