1. Tardigrade
  2. Question
  3. Mathematics
  4. 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.

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Q. 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.

Percentages, Profit and Loss, Discount and Partnership

Solution:

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}{6 q}=\frac{4}{5} $
$\Rightarrow q=10 \text { months } $
$\frac{48}{9 r}=\frac{4}{6}$
$\Rightarrow r=8 \text { months }$