In this post we will try to solve questions related to partnership. These questions are easy to solve and involve knowledge of basic arithmetic.

Apart from its relevance for competition exams, the concept of partnership is important for your practical life as in future you will do work which will involve multiple partners. This chapter will provide you tools on how to share business resources if the work involves multiple partners.

**Partnership Aptitude Questions & Answer**

**Qu.1) A started a business with Rs. 45,000 and B joined afterwards with Rs. 30,000. If the profit at the end of the one year was divided in the ratio 2: 1 respectively, then B would have joined A for business after.**

**Sol**. Given: Capital of A = Rs. 45000 = C1

Capital of B = Rs. 30000 = C2

Ratio of profits = P1 : P2 = 2: 1

Time of A = 12 month = T1

To find = Time of B = T2

Now. By using the formula,

** C1 T1/ C2 T2 = P1/ P2**

45000 x 12/ 30000 x T2 = 2/ 1

45000 x 12 = 2x (30000 x T2)

45000 x 12/ (2 x 30000) = T2

T2 = 9 months

I.e., B would have joined after (12 – 9) = 3 Months.

**Ans. B would have joined after 3 months.**

**Qu.2) Four milkmen rented a pasture. M puts to graze 16 cows for 3 months and N puts 20 cows for 4 months, O puts 18 cows for 6 months and P puts 42 cows for 2 months. If M’s share in rent be Rs. 2400, the rent paid by O is:**

**Sol. **Given: M share in rent = Rs. 2400 for time = 3 months and for = 16 cows

N time = 4 months for = 20 cows

O time = 6 months and for = 18 cows

P time = 2 months for 42 cows

Ratio of rent for:

M = 16 x 3 = 48

N = 20 x 4 = 80

O = 18 x 6 = 108

P = 42 x 2 = 84

I.e., = 48: 80: 108: 84 or 12: 20: 27: 21

According to the question, 12 units = Rs. 2400 (unitary methid)

1 unit = 2400/ 12 = 200

Therefore, for O, 27 units = 200 x 27 = Rs. 5400

**Ans.Rs. 5400 will be paid by O.**

**Qu.3) Two partners X and Y start a business by investing Rs. 50,000 and Rs. 40,000 respectively. What will be the ratio of their profits at the end of the year?**

**Sol**. Given: X Capital (C1) = Rs. 50000 Y capital (C2) = 40000

For time = 12 months or 1 year (T1 = T2)

Therefore, ratio of their profit = C1 T1/ C2 T2 = P1/ P2

P1/ P2 = 50000 x 1/ 40000 x 1

= 5/ 4

**Ans. The required ratio is 5: 4**

**Qu.4) X starts a business with Rs.25,000. After 4 months Y joins him with Rs. 20,000. What will be the ratio of their profit at the end of the year?**

**Sol.** Given: X capital (C1) = Rs, 25000 Y Capital (C2) = Rs. 20000

T1 = 12 months and T2 = 12 – 4 = 8 months

To find: Ratio of profits = P1: P2

Now, C1 T1/ C2 T2 = P1/ P2

25000 x 12/ 20000 x 8 = P1/ P2

P1/ P2 = 15: 8

Ans. Hence the required ratio is 15: 8.

**Qu.5) A starts a business with 21000 /- and later on B joins him with 36,000/- After how many months did B join if the profit is distributed in equal ratio?**

**Sol**. Given: C1 = 21000 C2 = 36000

P1 = P2

T1 = 12 months

Now, C1 T1/ C2 T2 = P1/ P2

21000 x T1/ 36000 x T2 = 1

21000 x 12 = 36000 x T2

T2 = 21000 x 12/ 36000

T2 = 7 months

I.e., B joins after = 12 – 7 = 5 months

**Ans. Hence, B joins business after 5 months.**

**Qu.6) Mr. Rakesh opened a workshop investing Rs. 40,000. He invested additional amount of Rs. 10,000 every year. After two years his Student Bhuvnesh joined him with an amount of Rs. 85,000. Thereafter Bhuvnesh did not invest any additional amount. On completion of four year from the opening of workshop they earned an amount of Rs. 1,95,000. What will be Rakesh’s share in the earning.**

**Sol.** Given: Total investment of Rakesh Yadav in 4 years = Rs. 40000 + Rs. 50000 + 60000 + Rs. 70000 (since he invested 10000 additionally every year)

= Rs. 220000

Bhuvnesh investment = Rs. 85000 x 2 (for 2 years) = Rs. 170000

Time for this investment = 4 year

C1 : C2 = 220000: 170000

= 22: 17

According to the question,

(22 + 17) units = Rs. 195000

39 units = 195000

1 unit = 195000/ 39 = 5000

Rakesh Yadav investment = 22 units = 5000 x 22

= Rs. 110000

**Ans. Rakesh Yadav earning is Rs. 1,10,000.**

**Qu.7) X and Y enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, X withdraws. If they receive the profit in the ratio 5: 9, Find how long Y’s capital was used.**

**Sol**. Given: C1: C2 = 5: 6, P1: P2 = 5: 9

T1 = 8 months

To find: T2

Now, (C1 x T1) / (C2 x T2) = P1 : P2

5 x 8/ 6 x T2 = 5/ 9

T2 = 5 x 8 x 9/ 6 x 5

= 12 months

**Ans. Y’s capital used for 12 months.**

**Qu.8) Two partners invest Rs. 125,000 and Rs. 85000 respectively in a business and agree that 60% of the profit should be divided equally between them and the remaining profit is to be divided into ratio of their capitals. If one partner gets Rs. 300 more than the other, Find the total profit made in the business.**

**Sol. ** Given: C1: C2 = 125000: 85000

= 25: 17 (they have difference of 8)

According to the question, 60% of profit is divided between them

8 units = Rs. 300

1 unit = 300/ 8

(25 + 17 = 42) units = 300 x 42/ 8

40 % of profit = 300 x 42/ 8

100 % of profit = 300 x 42 x 100 / 8 x 40 (unitary method)

= Rs. 3937.50

**Ans. Total Profit = Rs. 3937.50 **

**Qu.9) A, B and C enter into a partnership with capitals in the ratio 5: 6: 8, at the end of the business term, they received the profit in the ratio 5: 3: 12. Find the ratio of time for which they contributed their capitals?**

**Sol**. C1: C2 : C3 = 5: 6: 8

P1: P2: P3 = 5: 3: 12

Since, C x T = P

Therefore, Ratio of time = P/ C

I.e., T1: T2: T3 = C1/ P1: C2/ P2: C3/ P3

= 5/5: 3/ 6: 12/8

= 1: ½: 3/2

= 2: 1: 3

**Ans. Ratio of their time is 2: 1: 3**

**Qu.10) X and Y entered into a partnership, investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months X withdrew Rs. 5000, while Y invested 5000 more. After 3 months more Z joins the business with a capital of Rs. 21,000. After a year they obtained a profit of Rs.26,400. By what amount does the share of Y exceeds the share of Z.**

**Sol.**Total investment by X in a year = Rs. 16000 x 3 + 11000 x 9 = Rs. 147000

Total investment by Y in a year = 12000 x 3 + 17000 x 9 = Rs. 189000

Total investment by Z in a year = 21000 x 6 = Rs. 126000

Now, C1: C2: C3 = 147: 189 : 126 = 7: 9: 6

According to the question, C x T = P (Since time is taken as 1 year)

(7 + 9 + 6) units = Rs. 26400

1 unit = 26400/ 22 (unitary method)

= Rs. 1200

Required difference = (9 – 6) x 1200

= 3 x 1200

= Rs. 3600

**Ans. Required difference is Rs, 3600**