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Quantitative Aptitude > Partnership :
Question 1.

A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?

Options:
  1.    Rs. 45
  2.    Rs. 50
  3.    Rs. 55
  4.    Rs. 60
Answer: Option A

A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.

Therefore C's rent = Rs.   \(\left(175\times\frac{9}{35}\right)\) = Rs. 45.


Question 2.

 and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

Options:
  1.    3 : 5 : 2
  2.    3 : 5 : 5
  3.    6 : 10 : 5
  4.    Data inadequate
Answer: Option C

Let the initial investments of A and B be 3x and 5x.

A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.


Question 3.

A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew  \(\frac{1}{4}\) of his capital and B withdrew  \(\frac{1}{5}\) of his capital. The gain at the end of 10 months was Rs. 760. As share in this profit is:

Options:
  1.    Rs. 330
  2.    Rs. 360
  3.    Rs. 380
  4.    Rs. 430
Answer: Option A

A : B = \(\left[4x\times3+\left(4x-\frac{1}{4}\times4x\right)\times7\right] : \left[5x\times3+\left(5x-\frac{1}{5}\times5x\right)\times7\right] \)

= (12x + 21x) : (15x + 28x)

   = 33x :43x

   = 33 : 43.

Therefore A's share = Rs. \(\left(760\times\frac{33}{36}\right)\)  =  Rs. 330.

 


Question 4.

A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?

Options:
  1.    4 months
  2.    5 months
  3.    6 months
  4.    8 months
Answer: Option D

Suppose B joined for x months. Then,

Then, \(\left(\frac{85000\times12}{42500\times x} = \frac{3}{1}\right )\)

 x = \(\left(\frac{85000\times12}{42500\times 3} = \frac{3}{1}\right ) = 8\)

So, B joined for 8 months.


Question 5.

Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?

Options:
  1.    7 : 6 : 10
  2.    12 : 15 : 16
  3.    42 : 45 : 56
  4.    Cannot be determined
Answer: Option B

Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.


Question 6.

Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?

Options:
  1.    Rs. 890
  2.    Rs. 1335
  3.    Rs. 1602
  4.    Rs. 1780
Answer: Option A

Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)

= 48 : 32 : 64

= 3 : 2 : 4.

Therefore Kamal's share = Rs.\(\left(4005\times\frac{2}{9}\right)\)  = Rs. 890.