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6. A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? | |

A. 6 months | B. 5 months |

C. 8 months | D. 7 months |

Discuss |

answer with explanation

Answer: Option C

Explanation:

Let B joined for $x$ months. Then

$85000×12:42500×x=3:1\\ \Rightarrow 850×12:425x=3:1\\ \Rightarrow 850×12×1=3×425x\\ \Rightarrow 850×4=425x\\ \Rightarrow x=8$

7. A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join? | |

A. 5 months | B. 6 months |

C. 7 months | D. 4 months |

Discuss |

answer with explanation

Answer: Option D

Explanation:

Assume that C was there in the business for $x$ months

A:B:C

$=40000×12:60000×10:120000×x\\=40×12:60×10:120x\\=40:5×10:10x\\=8:10:2x\\=4:5:x$

C's share $=375000×\dfrac{x}{9+x}=\dfrac{375000x}{9+x}$

$\Rightarrow \dfrac{375000x}{9+x}=150000\\ \Rightarrow \dfrac{375x}{9+x}=150\\ \Rightarrow 15x=6(9+x)\\ \Rightarrow 5x=18+2x\\ \Rightarrow 3x=18\\ \Rightarrow x=6$

It means C was there in the business for 6 months. Given that B joined the business after 2 months. Hence C joined 4 months after B joined.

8. A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit? | |

A. 1600 | B. 1400 |

C. 1200 | D. 1500 |

Discuss |

answer with explanation

Answer: Option D

Explanation:

Assume that the total profit is $x$

Since 5% goes for charity, 95% of $x$ will be divided between A and B in the ratio $3:2$

Therefore, A's profit $=\dfrac{95x}{100}×\dfrac{3}{5}$

Given that A's share is Rs. 855. Therefore,

$\dfrac{95x}{100}×\dfrac{3}{5}=855\\ \Rightarrow \dfrac{95x}{100}=855×\dfrac{5}{3}=285×5=1425\\~\\ \Rightarrow x=\dfrac{1425×100}{95}\\=\dfrac{285×100}{19}=1500$

Hence the total profit = 1500

9. A, B and C invest in a partnership in the ratio: $\dfrac{7}{2},\dfrac{4}{3},\dfrac{6}{5}$. After 4 months, A increases his share 50%. If the total profit at the end of one year is Rs.21,600, then what is B's share in the profit? | |

A. Rs. 3000 | B. Rs. 5000 |

C. Rs. 2000 | D. Rs. 4000 |

Discuss |

answer with explanation

Answer: Option D

Explanation:

Ratio of the initial investment

$=\dfrac{7}{2}:\dfrac{4}{3}:\dfrac{6}{5}=105:40:36$

Therefore, let the initial investments of A, B and C be $105x, 40x$ and $36x$ respectively

A increases his share 50% after 4 months. Hence the ratio of their investments

$=(105x×4)+\left(105x×\dfrac{150}{100}×8\right)$ $:40x×12:36x×12$

$=105+\left(105×\dfrac{3}{2}×2\right)$ $:40×3:36×3$

$=105×4:40×3:36×3\\=35×4:40:36\\=35:10:9$

B's share = total profit × $\dfrac{10}{54}$

$=21600×\dfrac{10}{54}=4000$

10. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. | |

A. 1000 | B. 2660 |

C. 4000 | D. 2300 |

Discuss |

answer with explanation

Answer: Option B

Explanation:

A is a working member and for that, he receives 5% of the profit

= 5% of 7400 $=\dfrac{5×7400}{100}=370$

Remaining amount $=7400-370=7030$

Ratio of their investments

$=6500×6:8400×5:10000×3\\=65×6:84×5:100×3\\=13×6:84:20×3\\=13×2:28:20\\=13:14:10$

Share of B in the profit

$=7030×\dfrac{14}{37}=190×14=2660$

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