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26. In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs.157300 was their profit, how much amount did B receive? | |

A. 48400 | B. 48000 |

C. 48200 | D. 48600 |

Discuss |

answer with explanation

Answer: Option A

Explanation:

Assume that investment of C $=x$

Then, investment of A $=2x$

Investment of B $=\dfrac{4x}{3}$

A:B:C $=2x:\dfrac{4x}{3}:x$

$=2:\dfrac{4}{3}:1=6:4:3$

B's share $=157300×\dfrac{4}{6+4+3}$

$=157300×\dfrac{4}{13}=12100×4=48400$

27. P, Q and R started a business by investing Rs.120000, Rs.135000 and Rs.150000 respectively. Find the share of each, out of the annual profit of Rs.56700. | |

A. 17850, 18500, 22000 | B. 17850, 18900, 21000 |

C. 16800, 18900, 21000 | D. 16800, 18900, 22000 |

Discuss |

answer with explanation

Answer: Option C

Explanation:

P : Q : R = $120000:135000:150000$

$=120:135:150\\=24:27:30\\=8:9:10$

Share of P

$=56700×\dfrac{8}{27}=2100×8=16800$

Share of Q

$=56700×\dfrac{9}{27}=2100×9= 18900$

Share of R

$=56700×\dfrac{10}{27}=2100×10=21000$

28. If 4 (P's Capital) = 6(Q's Capital) = 10(R's Capital), then out of the total profit of Rs 4650, R will receive | |

A. 700 | B. 800 |

C. 600 | D. 900 |

Discuss |

answer with explanation

Answer: Option D

Explanation:

Let P's capital be $p$,

Q's capital be $q$,

and R's capital be $r$

Then

$4p=6q=10r\\2p=3q=5r \cdots(A)$

From (A),

$q=\dfrac{2p}{3}~~\cdots(1)\\r=\dfrac{2p}{5}~~\cdots(2)$

$p:q:r=p:\dfrac{2p}{3}:\dfrac{2p}{5}$

$=15:10:6$

R's share $=4650×\dfrac{6}{31}=150×6=900$

29. P, Q, R enter into a partnership. P initially invests 25 lakh and adds another 10 lakh after one year. Q initially invests 35 lakh and withdraws 10 lakh after 2 years. R's investment is Rs 30 lakh. In what ratio should the profit be divided at the end of 3 years? | |

A. 18:18:19 | B. 18:19:19 |

C. 18:19:18 | D. 19:19:18 |

Discuss |

answer with explanation

Answer: Option D

Explanation:

P : Q : R

$=(25×1+35×2):(35×2+25×1)$ $:(30×3)$

$=95:95:90\\=19:19:18$

30. P, Q, R enter into a partnership and their share are in the ratio $\dfrac{1}{2}:\dfrac{1}{3}:\dfrac{1}{4}$. After two months, P withdraws half of his capital and after 10 more months, a profit of Rs 378 is divided among them. What is Q's share? | |

A. 120 | B. 144 |

C. 114 | D. 134 |

Discuss |

answer with explanation

Answer: Option B

Explanation:

The ratio of their initial investment

$=\dfrac{1}{2}:\dfrac{1}{3}:\dfrac{1}{4}\\=6:4:3$

Let the initial investment of P, Q and R be $6x, 4x$ and $3x$ respectively.

A:B:C

$=(6x×2+3x×10):4x×12:3x×12$

$=(12+30):4×12:3×12\\=(4+10):4×4:12\\=14:16:12\\=7:8:6$

B's share $=378×\dfrac{8}{21}=18×8=144$

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