Quantitative Aptitude : Partnership Practice Problems with Solutions - Lesson 3

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

Note : Before taking this exercise, I request you to read the Lesson 1 and Lesson 2 from below links. Thank you. 

• Read Lesson 1 of Partnership from here
• Read Lesson 2 of Partnership from here

Example 16 : Varun, Sachin and Kowshi, enter into partnership. Varun puts Rs. 500 for 3 months. Sachin Rs. 650 for 8 months and Kowshik Rs. 300 for 11 months. They gain Rs., 840. Find the share of Kowshik.

1. Rs. 260.20
   
2. Rs. 277.20
3. Rs. 300.80
4. Rs. 126
5. None of these

Solution :

Varun, Sachin, Koushik's investments 500, 650, 300

Investment period = 3, 8, 11

Profit ratio 500 x 3 : 650 x 8 : 300 x 11

Total profit = Rs 840

Share of Koushik  = 33 parts

= (840/10) x 33 = 277.20


Example 17 : Rohitha, Sravya an dHarshitha enter into partnership. Rohitha advances Rs. 1200 for 4 months, Sravya Rs. 1400 for 89 months and Harshitha Rs. 1000 for 10 months. They gain Rs. 585 altogether. Find the share of Sravya. 

1. Rs. 225
2. Rs. 250
3. Rs. 252
4. Rs. 108
5. None of these

Solution :

Rohitha, Sravya, Harshika's investments   1200   1400   1000

Investment period    4    8    10

Profit ratio     1200 x 4 : 1400 x 8 : 1000 x 10

                              12  :   28  :  25

Total profit = 65 parts  = 585

Share of Shravya = 28 parts

= (585/65) x 28 = Rs. 252


Example 18 : Tina contributes Rs. 1500 and Rina Rs. 900 in a business. Tina is a sleeping partner and Rina gets 10% of the profit for management and the rest of the profit is divided in proportion of their capitals. If the profit is Rs. 800, what is the share of Rina ?

1. Rs. 450
2. Rs. 375
3. Rs. 360
4. Rs. 350
5. None of these

Solution :

Tina, Rina's investments    Rs. 1500    Rs. 900

Profit ratios                 5  :  3

Total profit = Rs. 800

Tina is sleeping partner so Rina get 10% in profit for management.

Rina's management profit = 800 x (10/100) = Rs. 80

Remaining profit = 800 - 80 = 720  = 1 part

Rina's share = management profit + capital profit (3 parts)

= 80 + (3/8) x 720

= 80 + 270  = 350 rs


Example 19 : Sneha began business with Rs. 4200 and was joined afterwards by Neha with Rs. 7200. When did Neha join if the profits at the end of the year were divided equally ?

1. After 7 months
2. After 4 months
3. After 5 months
4. After 8 ,pmtjs
5. None of these

Solution :

Let period 'x' 

Sneha, Neha investments    Rs. 4200   Rs. 7200

Investment period  12    (12-x)

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

From data profit are equal then

=>  4200 x 12  = 7200 x (12-x)

7 = 12 - x

x = 5


Example 20 : Anirudh began business with Rs. 6000 and was joined afterwards by Sumith with Rs. 8000. At the end of the year Sumith got one-third of the total profit. When did Sumith join ?

1. After 3 months
2. After 4 months 
3. After 8 months 
4. After 9 months
5. None of these 

Solution :

Let period x 

Anirudh, Sumith's investments     6000      8000

Investment period      12,  (12-x)

Profit ratio = 6000 x 12 : 8000 x (12-x)

If Sumith got one-third (1/3) then

Anirudh got 2/3rd of profit

=> Their profit ratio   (2/3) : (1/3)  =>  2:1

=> ((600 x 12) / (800 x (12-x))  = 2/1  [ratios are equal]

12 - x = (6 x 12) / (8 x 2)

=>  12 - x = 4.5

=> x = 7 1/2 years


Example 21 : Rashmi starts business with a capital of Rs. 1200. Arpitha and Tanvi join with some investments after 3 and 6 months respectivelyi. If at the end of a year, the profit is divided in the ratio 2 : 3 : 5 respectively. What is Arpitha's investment in the business ?

1. Rs. 2400
2. Rs. 1800
3. Rs. 3600
4. Rs. 6000
5. None of these

Solution : 

Let Arpitha investment x, Tanvi investment y.

Rashmi, Arpitha, Tanvi investments       1200          x             y

Investment period 12 (12 - 13) (12 - 6)

Profit ratio = 1200 x 12 : 9x : 6y

But, given ratio  2 : 3 : 5

Let do equal of above ratio's first two parts  = (1200 x 12) 9x  = 2/3

=> x = ( (1200 x 12) / (9 x 2)  ) x 3  = 2400


Example 22 : Sai Teja puts 1/2 of the capital for 1/2 of the time, Bhanu Teja puts 1/3rd of the capital for 2/3rd of the time and Charan Teja puts rest of the capital for the whole time. Find th ratio of their profits ?

1. 7 : 8 : 6
2. 6 : 7 : 9
3. 9 : 8 : 6
4. 2 : 4 : 8
5. None of these

Solution : 

Let total capital '1', whole time '1'

Sai, Bhanuteja, Charanteja's investment

1/2      1/3      1- (1/2 + 1/3)

1/2     1/3           1/6

Investment period  1/2     2/3    1


Profit ratio   1/4 : 2/9  : 1/6

=>  9 : 8 : 6


Example 23 : Sujan and Satwik entered into a partnership investing Rs. 25000 and Rs. 30000 respectively. After 4 months Subath also joined the business with an investment of Rs. 35000. What is the share of Subath in an annual profit of Rs. 47000 ?

1. Rs. 18000
2. Rs. 15000
3. Rs. 17000
4. Rs. 14000
5. None of these

Solution :

Sujan, Satwik, Subath investments  =   25000    30000    35000

Investment period    =    12     12     (12-4)

Profit ratio   =  25000 x 12  :  30000 x 12  :  35000 x 8

                                      15  :  18  :  14

Total profit = (15 + 18 + 14) = 47

parts = 47000

Subath's share : 14 parts  =  (47000 / 47) x  14  = 14000


Example 24 : Radhika and Deepika invest Rs. 3000 and Rs. 4000 respectively in a business. If Radhika douibles her capital after 6 months, in what ratio should Radhika and Deepika divide that year's profit ?

1. 9 : 10
2. 9 : 8
3. 3 : 4
4. 4 : 3
5. None of these

Solution :

Radhika's Capital = 3000 for 6 months  +  6000 for 6 months

                                =   18000 + 36000 = 54000

Deepika's Capital = 4000 x 12

months = 48000

profit ratio = 54000 : 48000

               9 : 8

shared by Aindree Mukherjee

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