Alligation and MixturesImportant terms:1) Alligation:
Rule of alligation enables us to find the ratio in which two or more ingredients at a given price must be mixed to produce a resultant mixture of desired price. 2) Mean Price:
It is the cost of unit quantity of a mixture. 3) Mixture:
Mixture is formed by mixing two or more quantities. It can be expressed in the form of percentage or ratio.
- 10 % of sugar in water
- A solution of water and sugar is 12 : 20, which means water : sugar = 12 : 20According to the rule of alligation:
When two ingredients are mixed,
If a vessel contains A liters of milk and if B litres of milk is withdrawn and replaced by water, and again if B litres of mixture is withdrawn and replaced by water and this operation is replaced n times in all, then
|Cheaper Quantity (X)|| = ||(C.P. of Y) – (Mean Price)|
|(Quantity of Y)||(Mean Price) – (C.P. of X)|
|(Quantity of milk left after nth operation)|| = ||(A – B)||n|
|(Initial quantity of milk)||A|
|Quantity of milk left after nth operation = A x ||[A(1 – (B/A))n]|
Simplified formula to calculate quantity of milk left after nth
operation = [A(1 – (B/A))n
]Tricks and Tips:1) Rule of alligation:
Points to Remember While Using the Rule of Alligation
|Ratio = ||(M – B)|| = ||(B – M)|
|(A – M)||(M – A)|
- The three values alligated should always represent the same variable and should have same units.
- alligation of 3 values of cost gives the ratio in terms of number and vice-versa.
- If two values of cost price and selling price of the mixture are given, then in such cases first calculate the cost price of the mixture and then allegate the 3 values of cost price.
- A and B represent concentration if the numerical is based on mixing of solutions.Question Variety
Type : 1 Based on Rule of Alligation
In what ratio must wheat A at Rs. 10.50 per kg be mixed with wheat B at Rs. 12.30 per kg, so that the mixture be worth of Rs. 11 per kg?
a. 13 : 5
b. 18 : 3
c. 17 : 5
d. 11 : 5View solution
Correct option :(a)
Convert Rs into paise, to make the calculation easy
The required ratio = 130 : 50 = 13 : 5
In what ratio must a shopkeeper mix Peas and Soybean of Rs. 16 and Rs. 25 per kg respectively, so as to obtain a mixture of Rs. 19.50 ?
a. 9 : 5
b. 7 : 5
c. 11 : 7
d. 12 : 8 View solution
Correct option: (c)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 5.50 : 3.50 = 11 : 7