### Quantitative Aptitude Topic of the day: Mixture and Alligation

1. Alligation

It is the process to find the solution of problems concerned with compounding/mixing of ingredients which differ in price or quality.
Simply put it is the rule used to find the ratio in which two or more ingredients at a given value must be mixed to produce a mixture of desired value

2. Mean Price
It is the cost price of the unit quantity of the mixture.

3. Useful Formulae
If two ingredients A and B of price x and y are mixed and the price of resultant mixture is M (mean price)then the rule of alligation gives the ratio (R) in which these ingredients are mixed

R=(M−y)/(x−M)

This formula can be visualised as:

Thus the required ratio is,

R=(M−y) / (x−M)= (y−M) / (M−x)

4. Replacement of Part of Solution Formula:

Many questions of Mixture and alligation section are based on the following formula:

Lets Assume a container contains a solution composed of different ingredients . Some quantity of solution is then taken out and it is replaced with one of the ingredients. This process is repeated n times then,

Final Amount of ingredient of solution that is not replaced

= Initial Amount×(Vol. after removal / Vol. after replacing)^n

This formula can also be applied to ratios.

Final ratio of ingredient not replaced to total

= Initial ratio *(Vol. after removal / Vol. after replacing)^n

Attempt the following questions to check your level of preparedness for ratio proportion questions in competitive exams. You can answer the questions in comments section. Also make sure you checkout tomorrow’s (September 11) Winner’s Curry Lunch update for solutions to these questions along with the formulae used in VIDEO format by our Subject Expert.

Question 1 : In what ratio must water be mixed with milk to gain 25% on selling the mixture at cost price?

A) 4:01
B) 1:04
C) 3:02
D) 2:03

Question 2: Two vessel contains milk and water mixed in the ratio of 2:3 and 3:4. Find the ratio in which these two are to be mixed to get a new mixture in which ratio of milk to water is 7:10 respectively.

A) 10:07
B) 7:03
C) 5:03
D) 3:05

Question 3: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

A) 1/5
B) 1/10
C) 2/5
D) 2/10

Question 4: A shopkeeper has a mixture of 24 kg of sugar of worth Rs. 35 per/kg with another quality of sugar of Rs.42 a kg. By selling the mixture at Rs. 41.04 per kg, he may gain 8%, how much sugar of second quality, had added in the mixture.

A)18 kg
B) 32 kg
C) 16 kg
D) 28 kg

Question 5: In what ratio must wheat at Rs.3.20 per kg be mixed with wheat at Rs.2.90 per kg so that the mixture be worth Rs.3.08 per kg?

A)3:04
B) 3:03
C) 3 : 02
D) 4:05
VIDEO SOLUTIONS FOR SEPTEMBER 9 Ratio and Proportion QUESTIONS:

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