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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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