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**“One Topic, to rule them all”**

Alligation is a method of solving arithmetic problems related to mixtures of ingredients. Please note that alligation method is applied for percentage value, ratio, rate, prices, speed, etc. and not for absolute value.** That is whenever per cent, per km, per hour, per kg, are being compared, we can use Alligation.**

**Common trick for Ratio-Proportion and Mixture Alligation : **Almost 50% of the questions are solvable just by going through the options. Just go through the questions I have solved in this article and you will know the approach.

__Rule of Alligation__**Ingredient A : Ingredient B = M – Y : X – M**

**Here Mean Price is something which applies on the whole thing. If two varieties of tea costing Rs. X and Rs. Y respectively are mixed and sold at Rs. Z, then Z is the mean price because it is price of the mixture.**

**Now I will take up some SSC CGL questions of Ratio-proportion and Mixture-Alligation.**

**Q.1**

Given SP = Rs. 320/kg, Profit = 20%

Hence CP = 320/1.2 = Rs. 800/3

So the Mean price is Rs. 800/3 per kg

Now you can apply the formula-

Type 1 : Type 2 = 280 – 800/3 : 800/3 – 180 = 2 : 13

**Answer : (B)**

**
**Both the containers have equal capacity. Let us assume that both containers are of 28 litres. Why 28? Because 28 is the LCM of (3 + 1) and (5 + 2) or 4 and 7. So taking the capacity as 28 litres will make your calculations easier.

In Container 1, we have (3/4)*28 = 21 litres of milk and (1/4)*28 = 7 litres of water.

In Container 1, we have (5/7)*28 = 20 litres of milk and (2/7)*28 = 8 litres of water.

Total milk in both the containers = 21 + 20 = 41

Total water in both the containers = 7 + 8 = 15

Milk : Water = 41 : 15

Answer : (D)

__Shortcut__Container 1 has 3 times more milk than water

Container 2 has 2.5 times more milk than water

When the contents of the two containers are mixed, the milk will still be more than water. How much more ? Somewhere between 2.5 and 3 times

(D) is the only option where the quantity of milk is around 2.7 times (i.e. between 2.5 and 3) that of the water.

Milk in vessel A = 4/7

Milk in vessel B = 2/5

Milk in vessel C = 1/2 (because in vessel C, milk and water are present in 1:1 ratio)

You have to mix 4/7 and 2/5, to produce 1/2. Hence 1/2 is the Mean Price.

A : B = (1/2 – 2/5)/(4/7 – 1/2) = 14 : 10 = 7 : 5

__Shortcut__

Final ratio of the three varieties is 5 : 7 : 9

The question asks us the quantity of third variety of tea in the final mixture. From the above ratio, it is clear that the quantity of the third variety is a multiple of 9. So 45 is the only option possible.

**Answer : (D)**

__Method__

Let the three quantities be 4x, 5x and 8x

New quantities are 4x + 5, 5x + 10 and 8x + p

Now 4x + 5 : 5x + 10 : 8x + p = 5 : 7 : 9

(4x + 5)/(5x + 10) = 5/7 and (4x + 5)/(8x + p) = 5/9

Solving 1st equation, we get x = 5

Solving 2nd equation, we get p = 5

In the final mixture the quantity of the third variety is 8x + p = 8*5 + 5 = 45

In this question we will use the below formula

So from the above formula

(Quantity of acid left)/(Quantity of acid in the original mixture) = (1 – 4/20)^2 = 16:25

**Answer : (A)**

Let the original quantities of A and B be 4x and x

In 10 litres, quantity of A = 4/5 * 10 = 8 litres

In 10 litres, quantity of B = (10 – 8) = 2 litres

New quantities of A and B are 2x and 3x

(Original Quantity of A) – (New quantity of A) = 8 litres[Because after taking out 10 litres of the mixture, the quantity of liquid A reduced by 8 litres]
So, 4x – 2x = 8

or x = 4

Hence quantity of liquid A in original mixture = 4*4 = 16 litres

**Answer : (C)**

**Note : **In the above question, there were two different ratios 4:1 and 2:3, then too I took the same constant of proportionality for them, i.e. ‘x’ because the following two conditions were met:

1. The volume of mixture did not change (Like in this question 10 litres were replaced, not removed)

2. The two ratios had same no. of parts (4:1 and 2:3 both have 5 parts)

You can take different constant to solve the question, but that will make the calculations little lengthy.

Since the ratio of alcohol and water is 1:4, hence quantities of alcohol and water in the mixture are 3 litres and 12 litres respectively.

Total volume will become 18 litres after adding 3 litres water

% of alcohol = 3/18 * 100 = 50/3%

**Answer : (B)**

**Q. 8) **

__Shortcut__

**Answer : (C)**

__Method__

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