Partnership
Alligation or Mixture & Partnership
Alligation or Mixture :
Mixing ratio of two things are called Alligation or Mixture , In which two things one thing is costly and second thing cheap.
Quantity of cheap thing
-------------------------------------
Quantity of costly thing
cost of 1 unit costly thing - average cost
= --------------------------------------------------------------
average cost - cost of 1 unit cheap thing
Example :
1) cost of rice Rs 15/kg and cost of rice Rs 25/kg .In which ratio we mix both rice then cost of mixture will be Rs 21.50 ?
Sol.
25 - 21.50
= ------------------
21.50 - 15
3.50
= ---------------
6.50
7
= ----------
13
= 7 : 13
2) Rule :
If we take x litre liquid from a liquid and we mix x litre of water in a liquid . This repeat n time than remain liquid
( Total liquid - x )^n
= Total liquid -----------------------------
( Total liquid )^n
Example :
We take 1 litre milk from 20 litre of milk and mix 1 litre water . After that we take 1 litre from this mixture and mix 1 litre water . At the end how much mixture we get ?
Sol.
(Total Milk - x )^n
Remain milk = Total Milk----------------------------
( Total Milk)^n
( 20 - 1 )^2
= 20 X------------------
( 20)^2
19X19
= 20 X--------------
20X20
19 X 19
= ----------------
20
361
= -------------
20
= 15.3 liter
3) Rule :
If we take x litre liquid from a liquid and we mix x litre of water in a liquid again we take y litre liquid and mix y litre water .
Remain quantity of liquid
(Total liquid - x)(Total liquid-y)
= Total liquid -----------------------------------------------
(Total liquid)(Total liquid)
4)Rule :
We mix water in milk , it sell on cost price than we get x% profit
water x
---------- = -------
milk 100
5) Rule :
x% milk in mixture of M gram milk and water . we add milk to increase its quantity y% .
M ( y - x )
= ----------------
100 - y
6) Rule :
x% milk in mixture of M gram milk and water . we heated water ,to decrease its quantity y%.
M ( x - y )
= ---------------
100 - y
Partnership
When two or more than two persons run a business jointly , they are called partners and the deal is known as partnership .
a) Rule :
When investments of all the partners are for the same time , the profit or loss is divided among them in the ratio of their investments.
b) Rule :
When investments are for different times, then equivalent capitals are calculated for a unit of time by multiplying the capital with the number of units of time .
Gain or loss is now divided in the ratio of these capitals .
Remark :
A partner who manages the business is called a working partner and the one who simply invests the money is called a sleeping partner.
7) Rule :
If two person X and Y are partner than
Dividend of X
----------------------
----------------------
Dividend of y
Investment of X x Investment time of X
= ---------------------------------------------------------------
Investment of y x Investment time of y
8) Rule :
If X ,Y , Z Invest for time t1 ,t2 , t3 than
Profit Ratio of X , Y , Z = X : Y : Z
=(Investment of X x t1 ) : ( Investment of Y x t2 ) : ( Investment of Y x t3 )
Example :
1) Rakesh start business with invest Rs 10000 . After four month Rajesh joined him with an investment Rs 8000 . At the end of the year dividend Rs 4600 . what will the part of Rajesh.
Sol .
Dividend of Rakesh 10000x12
-------------------------------- = ------------------
Dividend of Rajesh 8000x8
60
= -----------
32
15
= ------
8
ATQ
15 + 8 = 23
Part of Rajesh = 4600
------------ X 8
23
= 1600
2) Deepak and rajesh started a business by investing Rs 54000 and Rs 25500 respectivly . Find the share of each out of an annual income of Rs 21200 .
Sol .
Ratio of share of Deepak and Rajesh
= 54000 : 25500
= 36 : 17
sum of ratio 36 +17 = 53
36
Share of Deepak = Rs 21200 x----- =Rs 14400
53
17
Share of Rajesh = Rs 21200 x---- = Rs 6800
53
3) A, B, C hire a meadow for Rs 2520. If A puts in 20 cows for 8 days, B puts 25 cows for 8 days and C puts 16 cows for 9 days . Find the rent to be paid by each .
Sol.
Ratio of consumption made by A, B, C
= (20X8 : 25X8 : 16X9 )
=160 : 200 : 144
=20 : 25 : 18
Sum of the ratio = 20 + 25 + 18 = 63
20
A's share =Rs 2520X----- = Rs 800
63
25
B's share =Rs 2520X---- = Rs 1000
63
4) Suresh started a business by investing Rs 65000 . After 4 months Anil joined him with some investment . At the end of the year, the total profit was divided between them in the ratio 2 : 3 . How much was invested by Anil ?
Sol .
Suppose Anil invested Rs . x Then
65000 X 12 2
------------------- = -----
x X 8 3
65000 X 12 X 3
x = -----------------------------
8 X 2
= 146250
Exercise
1)A, B and C enter into a partnership with a capital in which A's contribution is Rs 10000 . If out of a total profit of Rs 1000, A gets 500 and B gets Rs 300 Then C's capital is :
a) Rs 4000 b) Rs 5000 c) Rs 6000
d) Rs 9000
2)) Two persons P and Q start a business together P invests Rs 8000 If the shares of profit of P and Q be Rs 360 and Rs 450 respectively the investment of Q is :
a) 9000 b) 12000 c) 10000 d) 15000
3)If A's capital is equal to twice B's capital and B's capital is three times C's capital, then the ratio of their capitals is
a)2:1:3 b) 1:2:6 c) 6:3:1 d) 1:3:6
Answer 1) a 2) c 3) c
