Question

Three friends $P,Q$, and $R$ started a smallscale cloth house business with the initial investment ratio $4:6:9$, respectively, and the profit ratio at the end of a year is $4:5:6$. If $P$ withdraws her investment precisely after a year then which of the following is/are true for $Q$ and $R$ duration of the investment.

• A. $P$ invested for the longest duration
• B. $R$ invested for the shortest duration
• C. $Q$ invested for the longest duration
• D. $P$ invested for the shortest duration

Answer 1

Answer: (A), (B)

Ratio of investment $=4:6:9$
Let the investment period of $Q$ and $R$ be $q$ and $r$, respectively
At the and of year profit $=4\times 12:6\times q:9\times x$
We know $4\times 12:6\times q:9\times r=4:5:6$
$\frac{48}{6q}=\frac{4}{5}$
$\Rightarrow q=10\text{ months }$
$\frac{48}{9r}=\frac{4}{6}$
$\Rightarrow r=8\text{ months }$