Ratios & Proportion
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Q.

$A$, $B$ and $C$ enter into a partnership by investing Rs.3600, Rs.4400 and Rs.2800. $A$ is a working partner and gets a fourth of the profit for his services and the remaining profit is divided amongst the three in the rate of their investments. What is the amount of profit that $B$ gets if $A$ gets a total of Rs. 8000?

 A.

4888.88

 B.

9333.33

 C.

4000

 D.

3666.66

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Solution:
Option(A) is correct

Let $x$ be the profit.

$A$ is a working partner and gets a fourth of the profit for his services.

$\Rightarrow$ $A$ gets $\dfrac{1}{4}x$ of the profit.

$\Rightarrow$ Remaining profit $=x-\dfrac{1}{4}x=\dfrac{3}{4}x$

Their investment ratio = $3600:4400:2800=9:11:7$

Also, remaining profit is divided amongst the three in the rate of their investments.

$\Rightarrow$ $A$ will get extra, $\dfrac{9}{9+11+7} \times \left( \dfrac{3}{4}x\right)$

$=\dfrac{9}{27} \times \left( \dfrac{3}{4}x\right)$ 

$=\dfrac{1}{3} \times \left( \dfrac{3}{4}x\right)$ 

$B$ will get, $\dfrac{11}{9+11+7}\times  \left( \dfrac{3}{4}x\right)$

$=\dfrac{11}{27} \times \left( \dfrac{3}{4}x\right)$

$A$'s profit of Rs. 8000 = \(\dfrac{1}{4}\times x+\dfrac{1}{3}\times \left(\dfrac{3}{4}\times x\right)=\dfrac{1}{2}\times x\)

\(x = \text{Rs }16,000\)

Therefore $B$'s profit = \(\dfrac{11}{27}\times \left(\dfrac{3}{4}\times 16,000\right)=\text{Rs }4888.88\)


(2) Comment(s)


Rockstar
 ()

how 11/27 is coming?


Saikumar
 ()

$b's$ share out of total is $\dfrac{11}{9+11+7} = \dfrac{11}{27}$