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## Arithmetic: Partnership Test-2

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Question 1 |

A, B and C enter into a partnership. A invests some money at the beginning ,B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit be Rs.27000 C’s share is:

Rs.9000 | |

Rs.11250 | |

Rs.10,800 | |

Rs.8625 |

Question 1 Explanation:

Ratio of profit

$ \displaystyle \begin{array}{l}=x\times 12:2x\times 6:3x\times 4\\=1:1:1\\\therefore \,\,\,C's\,\,\,share=\frac{1}{3}\times 27000\\=Rs.\,9000\end{array}$

$ \displaystyle \begin{array}{l}=x\times 12:2x\times 6:3x\times 4\\=1:1:1\\\therefore \,\,\,C's\,\,\,share=\frac{1}{3}\times 27000\\=Rs.\,9000\end{array}$

Question 2 |

X, Y and Z were sharing profits in the ratio 4: 3: 2. Y retired from the firm and X and Z decide to share profits in the ratio 3: 2. Calculate the gaining ratio.

7: 8 | |

5: 9 | |

4: 7 | |

5: 8 |

Question 2 Explanation:

Gaining ratio

$ \displaystyle \begin{array}{l}=\left( \frac{3}{5}-\frac{4}{9} \right):\left( \frac{2}{5}-\frac{2}{9} \right)\\=\frac{27-20}{45}:\frac{18-10}{45}=7:8\end{array}$

$ \displaystyle \begin{array}{l}=\left( \frac{3}{5}-\frac{4}{9} \right):\left( \frac{2}{5}-\frac{2}{9} \right)\\=\frac{27-20}{45}:\frac{18-10}{45}=7:8\end{array}$

Question 3 |

Karan starts a business by investing Rs.60000. six months later Shirish joins him by investing Rs.100000. At the end of one year from commencement of the business, they earn a profit of Rs.151800. What is the Shirish’s share in the profit?

Rs.55200 | |

Rs.82800 | |

Rs.62500 | |

none |

Question 3 Explanation:

Ratio of the Profit = Ratio of the equivalent capitals of Karan and Shirish for 1 month

$ \displaystyle \begin{array}{l}=60000\times 12:100000\times 6\\=720000:600000=6:5\\\therefore \,\,\,Shirish's\,\,\,share\,\,\,in\,\,the\,\,\,profit\\=Rs.\,\left( \frac{5}{11}\times 151800 \right)=Rs.69000\end{array}$

$ \displaystyle \begin{array}{l}=60000\times 12:100000\times 6\\=720000:600000=6:5\\\therefore \,\,\,Shirish's\,\,\,share\,\,\,in\,\,the\,\,\,profit\\=Rs.\,\left( \frac{5}{11}\times 151800 \right)=Rs.69000\end{array}$

Question 4 |

Prakash, Sunil and Anil started a business jointly investing Rs.11 lakhs , Rs. 16.5 lakh and Rs. 8.25 lakhs respectively. The profit earned by them in the business at the end of three years was Rs.19.5 lakhs. What will be the 50% of Anil’s share in the profit?

Rs.4.5 lakhs | |

Rs.2.25 lakhs | |

Rs.2.5 lakhs | |

Rs.3.75 lakhs |

Question 4 Explanation:

Ratio of the equivalent capitals of Prakash, Sunil and Anil for 1 month

= 11 X 36: 16.5 X 36 : 8.25 X 36

= 4:6:3

Therefore Anil’s share in the profit

{3/(4+6+3)} X 19.5

= 4.5 lakh

Therefore 50% of 4.5

2.25 lakh

= 11 X 36: 16.5 X 36 : 8.25 X 36

= 4:6:3

Therefore Anil’s share in the profit

{3/(4+6+3)} X 19.5

= 4.5 lakh

Therefore 50% of 4.5

2.25 lakh

Question 5 |

Sonu invested 10% more than Mona. Mona invested 10% less than Raghu. If the total sum of their investment is Rs.5780, how much amount did Raghu invest?

Rs.2010 | |

Rs.2000 | |

Rs.2100 | |

Rs.2210 |

Question 5 Explanation:

Let Mona’s investment=Rs.100

Therefore Sonu’s investment = Rs.110

And Raghu’s investment

$ \displaystyle =Rs.\,\frac{1000}{9}$

Therefore Ratio of Mona’s, Sonu’s and Raghu’s investments

$ \displaystyle =100:110:\frac{1000}{9}=90:99:100$

Sum of ratios = 90 + 99 + 100 = 289

Therefore Raghu’s investment

$ \displaystyle =Rs.\,\left( \frac{100}{289}\times 5780 \right)=Rs.2000$

Therefore Sonu’s investment = Rs.110

And Raghu’s investment

$ \displaystyle =Rs.\,\frac{1000}{9}$

Therefore Ratio of Mona’s, Sonu’s and Raghu’s investments

$ \displaystyle =100:110:\frac{1000}{9}=90:99:100$

Sum of ratios = 90 + 99 + 100 = 289

Therefore Raghu’s investment

$ \displaystyle =Rs.\,\left( \frac{100}{289}\times 5780 \right)=Rs.2000$

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