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September 26, 2016

Quantitative Aptitude : Partnership Problems with Solutions - Lesson 2

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Hi friends, I am Aindree. In our previous lesson, we have learnt the Introduction of Partnership topic of Aptitude Section. Today we shall see some practice problems with explanations. Happy Reading :)

Note : Before reading these examples, please read the Introductory Lesson 1 from here for better understanding. Thank you :)

Example 6 : A, B and C investment in a partnership in the ratio of 5 : 6 : 8. Ratio of their profit is 5 : 3 : 12. Find the ratio of time for their investment ?

Solution :

Required Ratio = (5/5) : (3/6) : (12/8)

= 1 : (1/2) : (3/2)

= 2 : 1 : 3

Example 7 : Three people A, B and C invested money in a partnership in the ratio of 4 : 2 : 8 ratio of their time of investment is 3 : 3 : 2. What is the ratio of their profit ?

Solution :

Required ratio = 4 x 3 : 2 x 3 : 8 x 2

= 12 : 6 : 16

= 6 : 3 : 8


Example 8 : P, Q and R are partners in a business. P puts in Rs. 350,  Rs. 450 and R Rs. 550. What is the share of R in a profit of Rs. 405 at the end of the year ?
    Solution :
    P, Q, R's investments 350 : 450 : 550
    Profit ratio 350 : 450 : 550
    = 7 : 9 : 11
    Total Profit = 27 parts = 405
    R's profits = (405/27) x 11 = 165
      Example 9 : x and y enter into partnership. x contributed Rs.6,000 for 4 months and y Rs. 5,000 for 8 months. What is the share of profit of y out of Rs. 6,000 ?

      Solution :

      x, y's investments     6000    5000
      Investment period       4           8

      Profit ratio = >  6000 x 4 : 5000 x 8

      => 24 : 40 

      = >  3 : 5

      Total profit = 8 parts = 6000

      y's share = 5 parts = (6000/8) x 5 = 3750


      Example 10 : A, B and C enter into partnership. A puts in Rs. 1200 for 6 months, B Rs. 800 for 7 months and C Rs. 600 for 8 months. What is the share of A out of the profit Rs. 396 ?

      Solution :

      A, B, C's investments           12000          800          600
      Investment period                     6                7              8
      Profit ratio   72 : 56 : 48

                            9 : 7 : 6

      Total profit = 22 parts = 396

      A's share = 9 parts = (396/22) x 9 = 162

      Example 11 : Anita, Sunitha and Kavitha are three partners in a partnership. Anitha subscribe 1/3 of the capital and Sunitha 1/4 and Kavitha, the rest. What is the share of Kavitha in the total profit of Rs. 600 ? 

      Solution :

      Anita, Sunitha, Kavitha's investment

      =1/3, 1/4, 1 - [ (1/3) + (1/4) ]

      Profit ratio = 1/3 : 1/4 : 5/12

      Total profit = 12 parts = 600 = 4 : 3 : 5

      Share of Kavitha = 5 parts = (600/12) X 5 = 250

      Example 12 : Abhishikitha and Pranavi start a business with Rs. 7500 and Rs. 6000 respectively. Abhishikita is a sleeping partner and Pranavi gets 12.5% of the profit for managing the business. How should a profit of Rs. 1440 be divided between them ?

      Solution :

      Abhishikitha, Pranavi's invest 7500, 6000

      Profit ratio = 7500 : 6000

      = 5 : 4

      Abhishikita is sleeping partner, 

      So Pranavi's profit for managing business in total profit  = 1440 x 12.5% = Rs. 180

      Remaining profit = (5+4) parts  = 9 parts

      = 1440 - 180 = Rs. 1260

      Abhishikita's share

      = 1260 x (5/9) = Rs. 700

      Pranavi's share = 180 + 1260 x (4/9) = Rs. 740


      Example 13 : Sowmith began business with Rs. 4500 and was later joined by Mourya with Rs. 5400. WHen did Mourya join if the profits at the end of the year were divided in the ratio of 2 : 1 ?

      Solution :

      Let Mourya's joining time 'x'

      Sowmith, Mourya's investments           Rs. 4500          Rs. 5400
      Investment period               12          (12-x)

      Profit ratio = 4500 x 12 : 5400 x (12x)

      = 10 : (12 - x)

      But, given ratio  2 : 1

      =>  10/(12 - x) = 2/1

      12 - x = 10/2

      24 - 2x = 10

      => 2x = 14
      => x = 7

      Example 14 : Avinash began business with Rs. 4200 and was joined afterward by Nikhilesh with Rs. 7200. When did Nikhilesh join if the profits at the end of a year were divided equally ?

      Solution :

      Let period 'x'

      Avinash, Nikhilesh investments                 42000,    7200
      Investment period                      12    (12-x)

      Profit ratio = 4200 x 12 : 7200 (12-x)

      From data, profits are equal then

      => 4200 x 12 =7200 x (12-x)

      7 = 12-x

      x = 5

      Example 15 : Prabath and Rohith enter into partnership which capitals as 5 : 6. At the end of 8 months, Prabath withdraws; if they receive the profits in the ratio of 5 : 9, find how long Rohith's capital was used ?

      Solution :

      Let period 'x'

      Prabath, Rohith's investment ratio =  5 : 6

      Investment period 8 : x

      Profit ratio   40 : 6x

      given ratio = 5 : 9

      =>  40/6x = 5/9

      => x = 12

      shared by Aindree Mukherjee

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