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$P$,$Q$ and $R$ enter into a partnership with capitals in the ratio $3:2:1$. After 4 months, $P$ leaves the business and after 4 more months $Q$ also leaves the business and $R$ continues till the end of the year. If $R$ takes $10%$ of the profit for managing the business, then what part of the profit does $R$ get?









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Option(A) is correct

Let Rs 100 be the profit.

Rs 90 is to be divided in the ratio $12:16:12$. i.e $3:4:3$

$R$ gets \(\dfrac{3}{10}\times 90 =27\)and 10 for managing

Thus $27+10=37\%$

Edit: Thank you Deepak for providing a detailed solution in the comments.

(6) Comment(s)


When I open the comments window for a question I see the maths with the delimiters. Difficult to understand, especially in this case. Is there a setting I need to change?


I didn't quite understand this. Can someone pls explain? Thanks!


$P$, $Q$ and $R$ will share the profit in the ratio of their time and money invested $(\text{time} \times \text{money})$

Given that money invested by all three is in the ratio,


Now as given, $P$ has invested his money for 4 months

So, For $P$,

$\text{investment}=\text{time} \times \text{money}$

$=4 \times 3=12$

$Q$ has invested his money for 8 months.

So, For $Q$,

$\text{investment}=\text{time} \times \text{money}$

$=8 \times 2=16$

$R$ has invested his money for 12 months.

So, For $R$,

$\text{investment}=\text{time} \times \text{money}$

$=12 \times 1=12$

$\Rightarrow P:Q:R=12:16:12=3:4:3$.

Now, assume that total profit is 100 rs.

Out of this $10\%$ is more is given to $R$ for managing the business.

As per the given info, $R$ get $10\%$ to manage the business.

So, Actual profit = 90 rs.

Thus, $R$ gets total of,

$\Rightarrow 10\% + \left(\dfrac{3}{3+4+3}\times 90\right)\%$

$=10\%+\left(\dfrac{3}{10} \times 90\right)\%$

$=10\% + 27\%$

$=\textbf{37% profit}$

Vineethkumar Shenoi

@Shilpa Mishra-

Ratio of capital corresponding to P is "3" for 4 months and so his share would be 3x4 = 12

Q is staying in for 4 months more and so altogether 4+4 = 8months and so his share would be 2x8 = 16.

R is staying for the entire year and so his share would be 1x12 =12.

So we get the ratio 12:16:12.

Since no value is given for the total capital, we take it as 100, since for a percentage problem base is always taken as 100....

Now R takes 10% profit for managing and so 10% is deducted from 100 which is 90. This 90 is then shared between

P, Q, and R in the ration 12:16:12

Hope it's clear...

Shilpa Mishra

Where does the 12:16:12 ratio come from?

Where do Rs100 and rs90 Come from?

Please explain


hey it is only the assumption that 100 rs is profit ......