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# Partnership

1.

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 ?

Initial Ratio 4:5:6

Now, 4*8 +3*4 : 5*12 : 6*12

44:5*12 :6*12 ==> 11:15:18.

B’s share is Rs 7500

i.e. 15 7500

(11+15+18)44 ? ==>22000

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2.

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?

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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3.

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 ?

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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4.

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:

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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5.

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

30,000 : Q = 2 : 3

Q = 90,000/2 = 45,000

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6.

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?

Investment ratio 6:3:2

Month ratio 3:6:2

Then 6*3 : 6*3 : 2*2

18:18:4==>9:9:2

Both A and B gets equal and highest profits.

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7.

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 ?

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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8.

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?

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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9.

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 ?

Investments ratio is = 4:1

Time period ratio is = 2:1

Gain ratio of Naveen and Kannan = 8:1

Kannan got Rs. 5400,

1 5400 9 ? ==> Rs 48600

The total gain = Rs 48600

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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 ?

8p = 10q = 12r

4p = 5q = 6r

q = 4p/5

r = 4p/6 = 2p/3

P : Q : R = p : 4p/5 : 2p/3

15:12:10 R’s share = 2590 * (12/37) = 70*12 = Rs. 840.

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