Ratios & Proportion
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Q.

$A$, $B$ and $C$ enter into a partnership by investing Rs 28000, Rs 32000 and Rs 18000. $A$ is working partner and gets a fourth of the profit for this services and the remaining profit is divided amongst the three in the ratio of their investments. What is the amount of profit that $B$ gets if $A$ gets a total of Rs 4995?

 A.

Rs 1665

 B.

Rs 2960

 C.

Rs 2590

 D.

None of these

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Solution:
Option(B) is correct

Investment ratio among $A,B$ and $C$

$=28000:32000:18000$

$=14:16:9$

Suppose total profit $= \text{Rs. }x$.

$A$'s profit for his service = \(\text{Rs. }x\times \dfrac{1}{4}=\dfrac{\text{Rs. }x}{4}\)

Remaining profit = \(x-\dfrac{x}{4}=\dfrac{3x}{4}\)

$A$'s profit according to his investment: 

\(=\dfrac{3x}{4}\times \dfrac{14}{14+16+9}=\dfrac{7x}{26}\)

Then,

\(\dfrac{x}{4}+\dfrac{7x}{26}=\text{Rs. }4995\)

\(\Rightarrow \dfrac{13x+14x}{52}=\text{Rs }4995\)

\(\Rightarrow x=\text{Rs }9620\)

Hence, $B$'s profit = \(\dfrac{3x}{4}+\dfrac{16}{39}\)

\(\Rightarrow \left(\dfrac{3\times 9620}{4}\right)\times \dfrac{16}{39}=\text{Rs. }2960\)


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