Partnership Questions and Answers

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A, B and C started a business where their initial capital was in the ratio of 4:5:6. At the end of 8 months, A invested an amount such that his total capital became half to C’s initial capital investment. If the annual profit of B is Rs. 7500 then what is the total profit ?

A.Rs 22000
B.Rs 18000
C.Rs 20000
D.Rs 19500
E.None

Answer: A

Take the capitals as 4, 5 and 6, and the year as 12 months. A's capital changes after 8 months to half of C's initial 6, that is 3.

\[ A: 4 \times 8 + 3 \times 4 = 32 + 12 = 44 \]

\[ B: 5 \times 12 = 60 \]

\[ C: 6 \times 12 = 72 \]

\[ \text{total} = 176 \]

B's Rs. 7500 corresponds to 60 of those 176 parts:

\[ \text{total profit} = 7500 \times \frac{176}{60} = \text{Rs. } 22{,}000 \]

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X, Y and Z enter into a partnership and theirs shares are in the ratio 1/2 : 1/3 : 1/4. After two months, X withdraws half of his capital and after 10 months, a profit of Rs.420 is divided among them. What is Y’s share?

A.Rs 180
B.Rs 165
C.Rs 160
D.Rs 195
E.None

Answer: C

Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.

Let their initial investments be 6x, 2x and 3x respectively.

Ratio (6x * 2) + (3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 ==>7 : 8 : 6.

B’s share = 420 * 8/21 = Rs. 160.

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M and N are partners in a firm out of which M is sleeping partner and N is working partner. M invests Rs. 1,80,000 and N invests Rs. 90,000. N receives 14.5% of profit for managing the business and the rest is shared between both in ratio of their investments. M’s share in the profit of Rs. 24000 is ?

A.Rs 10100
B.Rs 11500
C.Rs 12520
D.Rs 13680
E.None

Answer: D

Profit received by N as working partner = 14.5% of Rs. 24000 = Rs. 3480

Balance in profit = 24000 - 3480 = Rs. 20520

Ratio of M and N =1,80,000 : 90,000 ==>2:1

Then M’s share 3 20520 2 ? Rs 13680

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Rupam and Ankita invest in a business in the ratio \(3 : 2.\) If \(5\)% of the total profit goes to charity and Rupam's share is \(Rs. 855,\) the total profit is:

A.Rs. 1425
B.Rs. 1500
C.Rs. 1537.50
D.Rs. 1576

Answer: B

Let the total profit be \(Rs. 100.\)

After paying to charity, Rupams's share \(= rs. (95 \times \frac{3}{5}) = Rs. 57.\)

If Rupam's share is \(Rs. 57,\) total profit \(= Rs. 100.\)

If Rupam's share \(Rs. 855,\) total profit \(= (\frac{100}{57} \times 855) = 1500.\)

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P and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.30000, the amount invested by Q is

A.Rs 40000
B.Rs 35000
C.Rs 45000
D.Rs 50000
E.None

Answer: C

With equal periods, profits divide in the ratio of the investments.

\[ \frac{30000}{Q} = \frac{2}{3} \quad\Longrightarrow\quad Q = \text{Rs. } 45{,}000 \]

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The investment of A is twice as that of B and thrice as that of C. B invested for twice the months than A and thrice the months than C. Who will earn the highest profit?

A.B
B.C
C.A
D.Both A and B
E.Both B and C

Answer: D

Profit shares are proportional to capital multiplied by time.

Take A's investment as 6 units, so B has 3 and C has 2. Let A's time be \( t \); then B's is \( 2t \) and C's is \( \tfrac{2t}{3} \).

\[ A: 6 \times t = 6t \]

\[ B: 3 \times 2t = 6t \]

\[ C: 2 \times \frac{2t}{3} = \frac{4t}{3} \]

A and B tie for the largest share, so both A and B earn the highest profit.

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P start a business with Rs. 10000, Q joins him after 2 month with 20% more investment than P, after 2 month R joins him with 40% less than Q. If the profit earned by them at the end of the year is equal to the twice of the difference between investment of P and ten times the investment of R. Find the profit of Q ?

A.Rs 35500
B.Rs 42000
C.Rs 38000
D.Rs 41100
E.None

Answer: C

P : Q : R = (10000 × 12) : (12000 × 10) : (7200 × 8) = 25 : 25 : 12

Now the Profit = 2 × (72000-10000) = 124000

Q’s share 25/62*12400=Rs 50000

Then profit of Q = 50000 - 12000 = Rs 38000.

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A, B and C start a business and their investments are in the ratio 4 : 3 : 6. Both A and B starts the business and C joins them after 6 months. It was decided that C will get a monthly salary of Rs 600 from the annual profits. C’s total salary came out to be 10% of the annual profit after a year. What is the share of B in the total profits?

A.Rs 8500
B.Rs 9720
C.Rs 9650
D.Rs 10100
E.None

Answer: B

C’s monthly salary Rs 600.

Then annual salary =600*6=3600 (Because he work for 6 month only)

Rs 3600 is 10% of total profit.

Then total profit is Rs 36000.

Ratio of their shares 4*12 : 3*12 : 6*6 = 4:3:3

Profit left after reducing salary of C = 36,000 - 3,600 = 32,400

B’s share 3/10*32400 = Rs 9720.

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Naveen and Kannan jointly started a business. Naveen invested four times as Kannan did and invested his money for double time as compared to Kannan. Kannan earned Rs. 5400. Then the total gain was ?

A.Rs 45000
B.Rs 48600
C.Rs 52000
D.Rs 55500
E.None

Answer: B

Naveen's capital-months are \( 4 \times 2 = 8 \) times Kannan's, so the profit splits \( 8 : 1 \).

\[ \text{Kannan's 1 part} = 5400 \]

\[ \text{total} = 9 \times 5400 = \text{Rs. } 48{,}600 \]

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10.

If 8 (P’s Capital ) = 10 ( Q’s Capital ) = 12 ( R’s Capital ) , then out of the total profit of Rs 2590 , R will receive ?

A.Rs. 740
B.Rs. 630
C.Rs. 700
D.Rs. 730
E.None

Answer: C

\[ 8P = 10Q = 12R \quad\Longrightarrow\quad P : Q : R = \frac{1}{8} : \frac{1}{10} : \frac{1}{12} \]

Multiplying through by 120:

\[ 15 : 12 : 10 \]

\[ \text{total parts} = 37, \qquad \frac{2590}{37} = 70 \]

\[ R = 10 \times 70 = \text{Rs. } 700 \]

The largest capital belongs to P, since the smallest multiplier corresponds to the biggest share.

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