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Aptitude  Partnerships  Solved Problem 1     A, B, and C invested Rs 18000, Rs 24000, and Rs.36000 in business, respectively. What is...

# 02. Aptitude Questions with Solutions ---- PARTNERSHIPS Solved Problems

Aptitude  Partnerships  Solved Problem 1
A, B, and C invested Rs 18000, Rs 24000, and Rs.36000 in business, respectively. What is the ratio of shares of their profits?
a) 3 : 4 :5               b) 2 : 3 :6             c) 3 : 4 : 6            d) 2 : 5 :7    e) 3 : 5 : 8
Explanation:
The ratio of Profits = Ratio of the amounts invested
= 18000:  24000 :  36000
= 3 :  4 :  6

Aptitude Partnerships  Solved Problem 2
A and B enter into a partnership. A invests Rs 16000, and B invests Rs 20000. If the profit at the end of the year amounts to Rs  27000. What would be the share of B in the profit?
a) Rs 10000            b) Rs 110000          c)Rs 12000            d)Rs 15000      e)Rs 21000
Explanation:
The ratio of the investment of A and B is 16000: 20000 = 4: 5
So they have to share the profit in the ratio of 4: 5
B's share of profit =  $\frac{5}{9}$ X 27000 = 15000

Aptitude Partnerships  Solved Problem 3
A and B started a business by investing Rs. 90000, and Rs. 165000 respectively. Find the share of A, out of an annual profit of Rs.85000
a) Rs 30000          b)Rs 35000         c)Rs 55000         d)Rs 60000        e) Rs 62000
Explanation:
The ratio of profits = The ratio of investments
The ratio of their shares in the profit = 90000: 165000
= 6: 11
:. A' s share = Rs. [85000 x $\frac{6}{17}$]   = Rs. 30000

Aptitude  Partnerships  Solved Problem 4
A, B, and C invested Rs 40000, Rs 100000, and Rs 80000 respectively in a business. The net profit for the year was Rs 24200, which was divided in proportion to their investments. Find the amount of profit that C earned?
a)  Rs 8800            b) Rs 2200          c) Rs 5500         d)Rs 6000      e)Rs 7500
Explanation: Ratio of profits = Ratio of the capitals
=   40000 : 100000 :  80000
=  2 : 5 : 4
Share of C in the annual profit Rs 24200 = 24200 X $\frac{4}{11}$   =   Rs 8800

Aptitude  Partnerships  Solved Problem 5
A, B, and C invested their capitals in the ratio of 2:5:8. At the end of the year, the difference between the shares of A and C is Rs 3600, then what is the total profit and what is the share of B?
a) Rs 9000  , Rs 3000          b) Rs  12000, Rs 4500             c) Rs 6000, Rs 2500
d) Rs 8000, Rs 3250               e) None of these
Explanation :
Ratio of Profits = 2:5:8
A's profit = 2x    B's profit= 5x and C's profit = 8x
Difference between the share of A and C = (8x-2x) = 6x= Rs 3600
=> x=Rs 600
So , Total Profit = (2x +5x +8x)=15x= (15 x 600) = Rs 9000
B's share =  5x =(5 X 600) = Rs 3000.

Aptitude Partnerships  Solved Problem 6
A profit of  Rs 10400 is to be divided among the partners A,B and C. The ratio of their investments is $\frac{1}{2} :\frac{1}{3} :\frac{1}{4}$   . What is the share of B?
a) Rs 1800                 b) Rs 1600                 c ) Rs 3200         d) Rs 4000   e) Rs 6500
Explanation:
The ratio of the investments = $\frac{1}{2}$: $\frac{1}{3}$: $\frac{1}{4}$.
=$\frac{6}{12}$ : $\frac{4}{12}$: $\frac{3}{12}$
(Here 12 is the LCM of 2,3 and 4)
= 6: 4 : 3
Therefore the ratio of profits = 6: 4 : 3
Share of B in total profit Rs 10400 = 10400 x 4/13 = Rs 3200

Aptitude Partnerships Solved Problem 7
A and B are partners in a business. A invests Rs 20000 for 8 months, and B invests Rs 30000 for 6 months. They gain Rs 6800. What is the share of B?
a) Rs 3000                b)Rs 3600           c)Rs 4000             d)Rs 4500   e)Rs 8000
Explanation:
A and B invested their capital C1 and C2  for the periods T2 and C2, then the ratio of their profits = C1T1: C2 T2
A invests Rs 20000 for 8 months and B invests Rs 30000 for 6 months
The ratio of their profits = (20000 X 8) : (30000 X 6)
=8: 9
Share of B =   $\frac{9}{17}$ x Rs  6800 = Rs 3600

Aptitude Partnerships Solved Problem 8
A, B and C enter into a partnership. A invests Rs 7200 for 4 months, B invests Rs 2400 for the whole year and C invests Rs 3600 for 8 months. The share of B in the profit is Rs 2300. What is the total profit?
a) Rs 6900         b)Rs 6400             c)Rs 4600               d)Rs 13800   e) Rs 7800
Explanation :
If the capital C1 invested for the period T1, and the capital C2 is invested   for the period T2 and capital C3 is invested for the time period T3, then
The ratio of the profits = C1T1: C2 T2: C3T3
Therefore, the ratio of profits   A : B : C = (7200 X 4) : (2400 X 12) : (3600 X 8)
= 28800  :  28800 : 28800
= 1 : 1 : 1
Share of B= 1x = 2300
Total Profit = (1x +1x +1x) = 3x = (3 x Rs 2300) =Rs 6900

Aptitude Partnerships  Solved Problem 9
A, B, and C rented a pasture. A puts in 6 oxen for 12 months , B puts in 7 oxen for 8 months, and C puts in 8 oxen for 6 months. If the rent of the filed is Rs 792, What rent is paid by C?
a)  Rs 162                 b)Rs 324               c)Rs 216            d)Rs 252     e)Rs 220
Explanation :
A puts 6 oxen for 12months
B puts 7 oxen for 8 months.
C puts 8 oxen for 6 months.
Therefore ratio of rents =  (6 X 12) :  (7 X 8) : (8 X 6)
= 72 : 56 :48
= 9 : 7 : 6
The rent paid by C = Rs 792 X $\frac{6}{22}$    = Rs 216

Aptitude Partnerships  Solved Problem 10
A started a business by investing Rs. 55000. After 3 months, B joined him by investing  Rs. 60000. Out of an annual profit of Rs. 42000, find share A?
a) Rs 15500           b)Rs 17000               c)Rs 23100            d)Rs 18900   e)Rs 20000
Explanation:
Ratio of their capitals = (55000 x 12) : (60000 x 9)
= 660000: 540000.
= 11: 9
Share of A = Rs 42000 x $\frac{11}{20}$    = Rs 23100

Aptitude - Partnerships  Solved Problem 11
A and  B enter into a partnership and together starts a business with contributions of Rs 30000 and Rs 40000, respectively. After 4 months, C also joins them with the contribution of Rs 90000. After 9 months, B withdraws his contribution. At the end of the year, the profit is Rs 24000. What is the share of B in the total profit?
a)Rs 5000              b)Rs 6000            c)Rs 7000             d) Rs 8000        e) Rs 8500
Explanation:
If the capital C1 invested for the period T1, and the capital C2 is invested   for the period T2 and capital C3 is invested for the period T3, then
The ratio of the profits = C1T1: C2 T2: C3T3
The ratio of profits = (30000 x 12)  : (40000 x 9) : (90000 : 8)
= 36000 : 36000 : 72000
= 1 : 1 : 2
Share of B in the total profit = 24000 x $\frac{1}{4}$    =Rs 6000

Aptitude Partnerships  Solved Problem 12
A , B and C started a business each investing Rs. 20000. After 5 months A withdrew Rs. 5000, B withdrew Rs. 4000 and C invested Rs. 6000 more. At the end of the year, a total profit of Rs. 69900 was recorded. What was the share of B in the profit?
a) Rs  21200         b) Rs 20500          c) Rs 18000       d) Rs 19500     e)Rs 24500
Explanation:
The ratio of the capitals of A, B, and C.
=( 20000 x 5 + 15000 x 7) : (20000 x 5 + 16000 x 7) :(20000 x 5  + 26000 x 7)
= 205000 : 212000 : 282000 = 205 : 212 : 282
B's share = Rs. 69900 x $\frac{212}{699}$  = Rs. 21200

Aptitude - Partnerships  Solved Problem 13
A started a business with Rs. 21000 and is joined afterward by B with Rs. 36000. After how many months did B join, if the profits at the end of the year are divided equally?
a)  3 months         b) 4 months          c) 5 months        d) 6 months        e)7 months
Explanation:    Profit is shared at the end of the year.
So A stays in the business for 12 months
Let B stays in the business for x months.
They shared the profits equally, then P1: P2 = 1 : 1
If the capital C1 is invested for the period T1 and capital C2 is invested for the period T,  then                                                = $\frac{C1}{C2}$ X $\frac{T1}{T2}$
=> $\frac{1}{1}$ = $\frac{21000}{36000}$ X $\frac{12}{x}$
On solving, we get x = 7
B stays in the business for 7 months. Therefore B joined the business after 5 months
Aptitude   Partnerships  Solved Problem 14
A starts a business with Rs Rs 4,50,000. After 4 months, B joins the business. At the end of the year,  they share the profits in the ratio 9: 4. What is the capital of B?
a) Rs 200000            b) Rs 250000        c) Rs 300000        d) Rs 400000    e)Rs 420000
Explanation :
They share the profits at the end of the year.
A starts the business and stays in the business for 12 months.
B  joins the business after 4 months, then he stays in the market for 8 months.
Let the capital of B be x.
$\frac{P1}{P2}$ = $\frac{C1}{C2}$ X $\frac{T1}{T2}$
=> $\frac{9}{ 4}$  = $\frac{450000}{X}$   X $\frac{12}{4}$
=>  x= Rs 300000
The capital of B is Rs 300000

Aptitude Partnerships  Solved Problem 15
A invested an amount of Rs 50,000 in starting a business. After 6 months, B joined him with an amount of Rs 80,000. At the end of 3 years, they got a profit of Rs 24,500. What was the share of A?
a) Rs 10,000         b) Rs Rs 10,500      c) Rs 15,000        d) Rs 18,000   e) Rs 19,500
Explanation:
At the end of 3 years, they shared profits.
A started the business. So he was in the business for 36 months.
B joined the business after 6 months. So he was in the business for 30 months
Then ratio of their capitals = 36 x 50000 : 30 x  80000
= 3 : 4
A's share in the profit of Rs 24,500 = Rs 24,500 x $\frac{3}{7}$  = Rs 10,500
Aptitude Partnerships  Solved Problem 16
A , B, C, and D start a partnership business. A invests 1/3 of the capital, B puts $\frac{1}{4}$ of capital, C invests 1/5 of the capital, and D invests the remaining capital. Find the share of D out of a profit of Rs  18000?
a) Rs 4000           b)Rs 5000               c) Rs 6000          d) Rs 3900    e)Rs 4200
Explanation:
Total capital invested by A + B + C =  $\frac{1}{3}$ + $\frac{1}{4}$ +$\frac{1}{5}$
= $\frac{47}{60}$
D's capital = (1 -$\frac{47}{60}$) = $\frac{13}{60}$
The ratio of capitals of A, B , C and D = $\frac{1}{3}$ : $\frac{1}{4}$
= 20 : 15 : 12 : 13

Therefore , the share of D = Rs 18000 X  $\frac{13}{60}$

=  Rs 3900

Aptitude Partnerships  Solved Problem 17

A, B, and C start a partnership business by investing Rs 24000, Rs 30000, and Rs 36000, respectively. A is a working partner, and B and C are sleeping partners. .A gets 15% of the annual profit for his work. If B gets Rs 17000 and C gets  Rs 20400 respectively from the annual profit as their shares, then what amount does A get from the annual profit?

a) Rs 21000        b) Rs 23000            c) Rs 22.600       d) Rs 28000   e)Rs 27,500
Explanation:
The ratio of capitals of A,B and C = Rs 24000 : Rs 30000 : Rs 36000
= 4: 5 : 6
Here A is a working partner and B and C are sleeping partners.
So B and C get only profits as their shares and A gets profit and remuneration equal to 15% of the total  profit for his work
Profit ratio of B and C = Rs 17000 : Rs 20400 = 5 :6
A's share of profit = $\frac{4}{5}$  x 17000 = Rs 13600
85% of profit ( Because A takes 15% of profit as his share)
= (17000+ 20400+13600)
=  Rs 41,000
A's remuneration = 15% of total profit = $\frac{15}{85}$  x 51000  = Rs 9000
Total amount A gets =( Remuneration + profit)
= (Rs 9000 + Rs  13600 )
= Rs 22,600

For a better understanding of the solved problems on Partnerships, visit Concept of Partnerships - Important Formulae
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