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QUESTION: 1

A, B and C enter into a partnership and their shares are in ratio 1/2 : 1/3 : 1/4, after 2 months, A withdraws half of his capital and after 12 months, a profit of Rs 1050 is divided among them. What is B’s share ?

Solution:

Ratio of investments =1/2 : 1/3 : 1/4 , LCM of 2, 3, 4 = 12 ,multiply ratios with 12 we get 6 : 4 : 3 , so,initial investment be 6x, 2x and 3x so, we can write: A : B :C

=(6x X 2 + 3x X 10 ) : (4x X 12) :(3x X 12) = 7:8:6

B’s share= (8/21) x 1050 = 400

QUESTION: 2

A started a business with Rs. 21,000 and is joined afterwars by B with Rs. 36,000. After how many months did B join if the profits at the end of the year are divided equally?

Solution:

let B joined after x months

Then, 21000 x 12 = 36000 x (12 – x)36 = 180x = 5Hence, B joined after 5 months

QUESTION: 3

Anju and Bimal are partners in a business. Anju contributes 1 / 4 of the capital for 15 months and Bimal received 2 / 3 of the profit, for how long Bimal’s money was used ?

Solution:

Let total profit is x

Then Bimal’s share in profit= (2/3)x

so anju’s share in profit= x- (2/3)x =x/3

so,we get ratios of profit of Anju :Bimal :: 1:2

Let total capital invested be Rs P and Anju’s money was used for 15 months while Bimal’s money was used for b months .

then, (1/4)P X 15 divide by (3/4)P x b = 1/2 [ Capital x time =profit] so,we get b=10

Bimal’s money was used for 10 months

QUESTION: 4

In a business P and R invested amounts in the ratio 2 : 1, whereas the ratio between amounts invested by P and Q was 3 : 2 . If Rs. 2,236 was their profit, how much amount did Q receive ?

Solution:

P : Q = 3 : 2 , P : R = 2 : 1 [given] Q : P = 2 : 3 [reverse], Q : P = 4 : 6 [multiply by 2] Now, P : R = 2 : 1

P : R = 6 : 3 [multiply by 3] P : Q =6 : 4 [after x3] , So Q : P : R = 4 : 6 : 3

or, P : Q : R = 6 : 4 : 3

Q’s share= 4/13 x 2236=Rs.688

QUESTION: 5

A, B and C rent a land. A puts 10 tractors for 7 months, B puts 12 tractors for 5 months and C puts 15 tractors for 3 months . If the rent of the land is Rs. 175000, how much must C pay as his share of rent?

Solution:

A : B : C = 10 x 7 : 12 x 5 : 15 x 3

= 70 : 60 : 45

= 14 : 12 : 9.

∴ C’s rent = Rs. [175000 x 9/35] = Rs. 45000.

QUESTION: 6

P and Q started a partnership business investing some amount in the ratio of 3:5. R joined them after six months with an amount equal to that of Q. In what proportion should the profit at the end of one year be distributed among P, Qand R?

Solution:

Let the initial investments of P and Q be 3a amd 5a.

P : Q : R = (3a x 12) : (5a x 12) : (5a x 6) = 36 : 60 : 30 = 6 : 10 : 5.

QUESTION: 7

A and B established a firm together. A’s investment was thrice that of B’s. A also kept the investment for twice as much time as B. If B got a profit of 4000, what was the total profit?

Solution:

let B’s investment= X then A’s investment= 3X

lets tim for B = t then,A’s time= 2t

A:B

3X x 3t : X x t

6:1

B’s share= 1/7 x total = 4000

total=28,000

QUESTION: 8

A and B entered into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs. 26400 after one year by

Solution:

A:B: C = 16000 x3 + 11000×9:12000 x 3 + 17000 x 9:21000 x 6 = 147:189:126 = 7:9:6

Difference of B and C’s shares = Rs. [26400 x (9/22) — 26400 x (6/22)) = Rs. 3600.

QUESTION: 9

Ashok being the sleeping partner receives 1/10th of profit and the remaining is divided between pramod and prakash in the ratio of 1:2..If the difference between the profit shares of Ashok and Prakash is Rs.2000.What is pramod’s share in Rs.?

Solution:

let total profit =x

ashok’s share in profit is (1/10)x

remaining profit = x= (1/10)x= (9/10)x

pramod’s share= 1/3 x (9/10)x = (3/10 )x

Prakash’s share= 2/3 x (9/10)x = (6/10)x

ashok – prakash= (6/10)x -(1/10)x = (5/10)x

5/10 x = 2,000 so, x= 4000 pramod’s share= (3/10) x 4000=1200

QUESTION: 10

P and Q invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and P’s share is Rs. 855, the total profit is:

Solution:

Let the total profit be Rs. 100.

After paying to charity, A’s share = Rs. 95 x 3/5 = Rs. 57.

If A’s share is Rs. 57, total profit = Rs. 100.

If A’s share Rs. 855, total profit =(100/57) x 855 = 1500.

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