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## Arithmetic: Partnership Test-3

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Question 1 |

Gina invests Rs.48000 to start a business. Four months later Shrayon joins her by investing Rs.62000 and another two months later Deepika joins them both by investing Rs.80000. At the end of one year the business earns a profit of Rs.20661. What is Deepika’s share in the profit?

Rs.7668 | |

Rs.6603 | |

Rs.7240 | |

Rs.6390 |

Question 1 Explanation:

Ratio of the profits of Gina, Shrayon and Deepika

$ \displaystyle \begin{array}{l}=48000\times 12:62000\times 8:80000\times 6\\=48\times 12:62\times 8:80\times 6\\=36:31:30\\Sum\,\,\,of\,\,\,ratios\\=36+31+30=97\\\therefore \,\,\,Deepika's\,\,share\\=Rs.\,\left( \frac{30}{97}\times 20661 \right)\\=Rs.\,6390\end{array}$

$ \displaystyle \begin{array}{l}=48000\times 12:62000\times 8:80000\times 6\\=48\times 12:62\times 8:80\times 6\\=36:31:30\\Sum\,\,\,of\,\,\,ratios\\=36+31+30=97\\\therefore \,\,\,Deepika's\,\,share\\=Rs.\,\left( \frac{30}{97}\times 20661 \right)\\=Rs.\,6390\end{array}$

Question 2 |

Sunetra invested an amount of Rs.50.000 to start a software business. After six months Nikhil joined her with an amount of Rs.80.000. At the end of 3 years they earned a profit of Rs.24.500. What is Sunetra’s share in the profit?

Rs.14.000 | |

Rs.9423 | |

Rs.10.250 | |

none |

Question 2 Explanation:

The ratio of capital invested by each partner

i.e. Sunetra and Nikhil for 1 month in order to get the same profit is:

36 × 50000 : 30 × 80000 =3 : 4

Therefore share of Sunetra out of

$ \displaystyle \begin{array}{l}Rs.\,24500=Rs.\,\frac{3}{7}\times 24500\\=Rs.\,10,500\end{array}$

i.e. Sunetra and Nikhil for 1 month in order to get the same profit is:

36 × 50000 : 30 × 80000 =3 : 4

Therefore share of Sunetra out of

$ \displaystyle \begin{array}{l}Rs.\,24500=Rs.\,\frac{3}{7}\times 24500\\=Rs.\,10,500\end{array}$

Question 3 |

Ninad, Vikas and Manav enter into a partnership. Ninad invests some amount at the beginning. Vikas invests double the amount after 6 months and Manav invests thrice the amount invested by Ninad after 8 months. They earn a profit of Rs.45.000 at the end of the year. What is Manav’s share in the profit?

Rs.25.000 | |

Rs.15.000 | |

Rs.12.000 | |

Rs.9.000 |

Question 3 Explanation:

Let Ninad invest Rs. x.

Therefore Vikas’s investment = Rs. 2x

Manav’s investment = Rs. 3x

Ratio of the equivalent capitals for 1 month of Ninad, Vikas and Manav respectively

$ \displaystyle \begin{array}{l}=x\times 12:\,2x\times 6:\,4\times 3x\\=1:1:1\end{array}$

Clearly, the profit will be shared equally.

$ \displaystyle \begin{array}{l}\therefore \,\,\,\,Manav's\,\,\,share\\=Rs.\,\frac{1}{3}\times 45000=Rs.\,15000\end{array}$

Therefore Vikas’s investment = Rs. 2x

Manav’s investment = Rs. 3x

Ratio of the equivalent capitals for 1 month of Ninad, Vikas and Manav respectively

$ \displaystyle \begin{array}{l}=x\times 12:\,2x\times 6:\,4\times 3x\\=1:1:1\end{array}$

Clearly, the profit will be shared equally.

$ \displaystyle \begin{array}{l}\therefore \,\,\,\,Manav's\,\,\,share\\=Rs.\,\frac{1}{3}\times 45000=Rs.\,15000\end{array}$

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