Tips and Tricks and Shortcuts Allegations and Mixtures:-

Type 1. Tips for Allegations and Mixtures

In most of these questions , you are supposed to find the ratio , or any one of the values either M(mean price) , or C(C.P of cheaper) or D(C.P of dearer) where the other two values and the ratio is given.

To find that , we have the best trick for you.

When two commodities are mixed then , 

		Quantity of cheaper		=		C.P. of dearer(d) – Mean Price(m)
		Quantity of dearer				Mean price(m) – C.P. of cheaper(c)

This equation can also be developed using the pictorial diagram.

Question  : Two varieties of wheat are mixed in the ratio of 4:5. The price of the mixture is ₹15 per Kg. The price of the variety having lesser weight is ₹12 per Kg. Calculate the price of the other variety.

Solution:

First of all we will identify and substitute the values in the diagram

 Now substituting this in the formula

		Quantity of cheaper		=		C.P. of dearer(d) – Mean Price(m)
		Quantity of dearer				Mean price(m) – C.P. of cheaper(c)

		4		=		N – 15
		5				15 – 12

		4		=		N – 15
		5				3

So , 5N – 75 = 12

N = Rs. 17.4 per Kg

Type 2. Shortcuts, Tricks for Allegations and Mixtures

Calculate quantity of pure Liquid after ‘n’ successive operations:

If a Container contains ‘x’ units of pure liquid , and we replace the liquid with ‘y’  units of water :

Then after ‘n’ successive operations, the units of pure liquid left is

=		x		1 —	y		n		units.
					x

Below  is an example to explain this concept.

Question :  A vessel contains 60L of milk, out of which 15L litres of milk is taken out and replaced by water. This process is repeated two times. Find the amount of milk left in the container.

Solution

From the question we have ,

Total Milk (x)  = 60L

Milk taken out in one round (y) = 15L

No. of rounds (N) = 2

So , Using the above formula ,

Amount of milk left in the container 

=		x		1 —	y		n		units.
					x

=		60		1 —	15		2		units.
					60

=		60			3		2		units.
					4

Solving this we get the answer as 33.75L

Read Also: How to solve Allegations and Mixtures question