# Tips And Tricks And Shortcuts For Alligation And Mixtures

## Tips And Tricks For Alligation And Mixtures

Tips and Tricks for Alligation and Mixtures will be discussed on this page for solution of problems regarding the mixing of ingredients in a shortcut way. ### Tips and Tricks and Shortcuts Alligations and Mixtures:-

##### Type 1. Tips and Tricks for Alligation 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,

$\left ( \frac{ \text{ Quantity of Cheaper }}{\text{ Quantity of dearer }} \right ) = \left ( \frac{ \text{ C.P of Dearer (d) – Mean price (m)}}{ \text{ Mean price(m) – C.P. of cheaper(c) }} \right)$

This equation can also be developed using the pictorial diagram. ### Question 1:

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

$\left ( \frac{ \text{ Quantity of Cheaper }}{\text{ Quantity of dearer }} \right ) = \left ( \frac{ \text{ C.P of Dearer (d) – Mean price (m)}}{ \text{ Mean price(m) – C.P. of cheaper(c) }} \right)$

$\frac{4}{5} = \frac{(N – 15)}{(15 – 12)}$
$\frac{4}{5} = \frac{N – 15}{3}$

So , 5N – 75 = 12

N = Rs. 17.4 per Kg

##### Type 2: Shortcuts, Tips and Tricks for Alligation 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

$\left ( x \left( 1 – \frac{y}{x} \right)n \right)$

Below  is an example to explain this concept.

### Question 2:

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

=$\left ( x \left( 1 – \frac{y}{x} \right)n \right)$

=$\left ( 60 \left( 1 – \frac{15}{60} \right)2 \right)$

=$\left ( 60 \left( \frac{3}{4} \right)2 \right)$

Solving this we get the answer as 33.75L

### Question 3:

A dealer has 1000 kg sugar and he sells a part of it at 8% profit and the rest of it at 18% profit. The overall profit he earns is 14%. What is the quantity which is sold at 18% profit?

### Solution :

As per the rule of alligation,

Quantity of Dearer: Quantity of Cheaper = (18-14) : (14-8) = 4:6 = 2:3

Quantity of sugar sold at 18% profit = 3/5 × 1000 = 600kg

### Question 4 :

How much coffee of variety A, costing Rs. 5 a kg should be added to 20 kg of Type B coffee at Rs. 12 a kg so that the cost of the two coffee variety mixture be worth Rs. 7 a kg?

### Solution :

As per the rule of alligation,

Quantity of Dearer: Quantity of Cheaper = (12-7) : (7-5) = 5:2

Quantity of Variety A coffee that needs to be mixed ⇒ 5:2 = x:20

⇒ x =50 kg

### Question 5 :

A mixture of 20 kg of water and spirit contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?

### Solution :

Water = $\left ( \frac{10}{100} \right )\times100=2$ and spirit = 18kg.

In the second mixture:

75 kg spirit is contained in a mixture of 100 kg

18 kg spirit is contained in a mixture of $\left ( \frac{100}{75} \right )\times18=24kg$

So, water to be added=24-20=4 kg

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### 2 comments on “Tips And Tricks And Shortcuts For Alligation And Mixtures”

• Pooja

prepInsta we have come doubt so how to solve it? And in some question the % of answer is almost same for 2-3 option , so that time how to analyse which answer is correct? 18
• PrepInsta 4