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Important Formulae

Ratio of Divisions of Gains:

1. When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.

Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:

(A's share of profit) : (B's share of profit) = x : y.

2. When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.

Suppose A invests Rs. x for p months and B invests Rs. y for q months then,
(A's share of profit) : (B's share of profit)= xp : yq.

Practice Questions

1.

A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 and Rs. 1,50,000 Respectively. Find the share of A, out of an annual profit of Rs. 56,700.
A.16000B.16500
C.16800D.17000

Report! Answer!

Answer is: C

Ratio of shares of A,B and C = 120000 : 135000 : 150000
Ratio = 8 : 9 : 10
= 8+9+10 = 27
∴ A's share = Rs. (56700 x 8/27) = 16800

2.

Ram started a business investing Rs. 45000. After 3 months, Ramesh joined him with a capital of Rs. 60000. After another 6 months, Rakesh joined them with a capital of Rs. 90000. At the end of the year, they made a profit of Rs. 16500. Find the share Ramesh ?
A.6400B.6500
C.6600D.6700

Report! Answer!

Answer is: C

Ram invested his capital for 12 months, Ramesh for 9 months, rakesh for 3 months.
So, Ratio of capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)
= 540000 : 540000 : 270000
= 2 : 2 : 1.
So, Ramesh share = Rs. (16500 x 2/5) = Rs. 6600

3.

A, B and C enter into partnership. A invests 3 times as much as B invests and B invests two third of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B ?
A.1200B.1250
C.1300D.1350

Report! Answer!

Answer is: A

Let C capital = Rs. X.
Then B capital = Rs. 2/3 X
A capital = Rs. (3 x 2/3 X) = Rs. 2X
∴ Ratio of their capitals = 2X : 2/3 X : X
= 6 : 2 : 3
Hence, B share = Rs. ( 6600 x 2/11) = Rs. 1200.

4.

Four milkmen rented a pasture. A grazed 24 cows for 3 months, B 10 cows for 5 months, C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 720, Find the total rent of the field?
A.3100B.3150
C.3200D.3250

Report! Answer!

Answer is: D

Ratio of shares of A, B, C, and D = (24x3) : (10x5) : (35x4) : (21x3)
Ratio of A : B : C : D = 72 : 50 : 140 : 63
Let Total rent be Rs. X. Then, A's share = Rs. 72X/325
∴ 72X/325 = 720
⇒ X = (720 x 325)/72 = 3250

5.

A invested Rs. 76000 in a business. After few months, B joined him with Rs. 57000. At the end of year, the total profit was divided between them in the ratio 2 : 1. After how many months did B join ?
A.3 monthsB.4 months
C.5 monthsD.6 months

Report! Answer!

Answer is: B

Suppose B joined after X months.
Then, B's money was invested for (12 – x) months.
∴ (76000 x 12)/(57000 x (12-X)) = 2/1
⇒ 912000 = 114000 (12 – X)
⇒ 114 (12 – X) = 912
⇒ 12 – X = 8
⇒ X = 4
Hence B joined after 4 months.

6.

A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After one year, B invests another Rs. 270000 and C, at the end of 2 years, also invests Rs. 270000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of C ?
A.3600B.360000
C.36000D.3600000

Report! Answer!

Answer is: B

Let the initial investments of A, B and C be Rs. 3X, Rs. 2X and Rs. 4X respectively.
Then, (3X x 36) : [(2X x 12) + (2X + 270000) x 24] : [(4X x 24) + (4X + 270000) x 12] = 3 : 4 : 5
⇒ 108X : (72X + 6480000) : (144X + 3240000) = 3 : 4 : 5
∴ (108 X)/(72 X+6480000) = 3/4
⇒ 432 X = 216X + 19440000
⇒ 216 X = 19440000
X = 90000
C's initial investment = 4X = Rs. 360000.

7.

P and Q started a business investing Rs. 85000 and Rs. 15000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively.
A.73:3B.17:3
C.3:17D.13:17

Report! Answer!

Answer is: B

P:Q = 85000:15000 = 17:3

8.

Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
A.10000B.10500
C.11000D.11500

Report! Answer!

Answer is: B

Kamal : Sameer = (9000 x 12) : (8000 x 7)
⇒ Kamal : Sameer = 108 : 56 = 27 : 14
∴ Sameer's share = Rs. ( 6970 x 14/41 ) = Rs. 10500

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