Aptitude Discussion

Q. |
Shyam, Gopal and Madhur are three partners in a business. Their capitals are respectively Rs 4,000, Rs 8,000 and Rs 6,000. Shyam gets $20\%$ of total profit for managing the business. The remaining profit is divided among the three in the ratio of their capitals. At the end of the year, the profit of Shyam is Rs 2200 less than the sum of the profit of Gopal and Madhur. How much profit, Madhur will get? |

✖ A. |
Rs 1600 |

✔ B. |
Rs 2400 |

✖ C. |
Rs 3000 |

✖ D. |
Rs 5000 |

**Solution:**

Option(**B**) is correct

The ratio of profit of Shyam, Gopal and Madhur is $4000:6000:8000 = 2:4:3$.

Let the annual profit be $p$.

Then, Shyam will get $0.2p$ for managing the business.

And, remaining $0.8p$ will be distributed in the ratio of their capital.

Thus, from the remaining capital, Shyam will get,

$=\dfrac{2}{2+4+3} \times 0.8p = \dfrac{2}{9} \times 0.8p$

Gopal gets,

$=\dfrac{4}{2+4+3} \times 0.8p = \dfrac{4}{9} \times 0.8p$

and Madhur Gets,

$=\dfrac{3}{2+4+3} \times 0.8p = \dfrac{3}{9} \times 0.8p$

So Shyam's total profit,

$= 0.2p + \dfrac{2}{9} \times 0.8p$

Given, at the end of the year, the profit of Shyam is Rs 2200 less than the sum of the profit of Gopal and Madhur.

$\Rightarrow \dfrac{4}{9} \times 0.8p + \dfrac{3}{9} \times 0.8p - 2200 = 0.2p + \dfrac{2}{9} \times 0.8p $

\(\Rightarrow \dfrac{7}{9}\times 0.8p-\dfrac{2}{9}\times 0.8p-0.2p=2200\)

\(\Rightarrow p=9,000\)

Thus, Madhur's share,

$= \dfrac{3}{9} \times 0.8p$

$= \dfrac{3}{9} \times 0.8 \times 9,000$

\(=\text{Rs }2400\)

**Edit:** After a comment from **rrk** a typo has been corrected and the solution is explained in more detail.

**Edit 2:** Another typo has been corrected after it was pointed out by **Zoha Amjad.**

**Edit 3:** For an alternative solution, check the comment by **Ajay Choudhary.**

**Ajay Choudhary**

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**Zoha Amjad**

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$\Rightarrow \dfrac{4}{9} \times 0.8p + \dfrac{3}{9} \times 0.8p + 2200 = 0.2p + \dfrac{2}{9} \times 0.8p$

In the equation above please correct the sign used with 2200

It will be negative and will become positive by shifting to the other side.

change to

$\Rightarrow \dfrac{4}{9} \times 0.8p + \dfrac{3}{9} \times 0.8p = 0.2p + \dfrac{2}{9} \times 0.8p+ 2200$

Thank you Zoha, Made the changes.

**Rrk**

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please clearify $\dfrac{7}{8} \times 0.8 - \dfrac{2}{9} \times 0.8 - 0.2p=2200$

There was a typo in the solution which is now corrected.

Earlier, it was mentioned as,

$\dfrac{7}{\textbf{8}} \times 0.8 - \dfrac{2}{9} \times 0.8 - 0.2p=2200$

Correct equation will be (now corrected),

$\dfrac{7}{\textbf{9}} \times 0.8 - \dfrac{2}{9} \times 0.8 - 0.2p=2200$.

Solution has been made more explanatory, hope it clarifies all the doubts now.

**Jan**

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shouldn't it be 1500?because we have profit as a whole is 9000.and shyam will take out first 20%,after which remaining profit will be distributed according to their shares.

S:G:M=2:4:3

Let total profit be p

Shyam' managing profit 20% of p=0.2p

Remaining profit =0.8p

So we can write

G+M-S=2200

(.8p÷9)×4+(.8p÷9)×3-(.8p÷9)×2+0.2p=2200

Than p=9000

Shyam managing profit =.2p=1800

Remaining =7200

Mathur profit =(7200÷9)×3=2400