NIMCET Quantitative Aptitude – Mixtures and Alligation: Formulas, Shortcuts and Questions

Mixtures and Alligation is an important topic in quantitative aptitude that deals with combining two or more substances with different values, costs or concentrations. Questions from this topic involve finding the average value of a mixture, calculating the required mixing ratio and determining the concentration of different components.

For your NIMCET exam preparation, understanding ratios, percentages and averages will help you solve these questions. You can also refer to the NIMCET syllabus to understand the topics covered in the examination and plan your preparation.

What are Mixtures and Alligation?

A mixture is formed when two or more substances or groups with different properties are combined. These properties may include cost, average or concentration.

Alligation is a shortcut method used to calculate the ratio in which two ingredients should be mixed to obtain a desired average, price or concentration.

The resultant value always lies between the two original values. It is closer to the value of the ingredient present in a greater quantity.

Prerequisites for this topic:

• Ratios

• Percentages

• Averages

Weighted Average Formula

The weighted average formula helps calculate the resultant value when two groups with different values are mixed in given quantities.

Formula:

R=a1n1+a2n2n1+n2

Where:

• a1 = Value of the first group

• a2 = Value of the second group

• n1 = Quantity of the first group

• n2 = Quantity of the second group

• R = Resultant value

When quantities are given in a ratio, the formula becomes:

R=a1r1+a2r2r1+r2

Important observations:

• The resultant value is closer to the value of the group present in a greater quantity.

• When equal quantities are mixed, the resultant is the midpoint of the two values.

Example:

Rice costing Rs. 100/kg and Rs. 200/kg is mixed in the ratio 7:3. Find the average cost.

Using the weighted average formula:

R=100(7)+200(3)7+3

R=700+60010=Rs. 130/kg

Therefore, the average cost of the mixture is Rs. 130 per kg.

Alligation Method and Formula

The Alligation Method is used when the individual values and desired resultant value are given, and you need to find the mixing ratio.

Mixture and Alligation Formula:

RequiredRatio=(a2-R):(R-a1)

Where:

• a1 = Lower original value

• a2 = Higher original value

• R = Desired resultant value

Example:

Two types of oil costing Rs. 150 and Rs. 250 per litre are mixed to obtain a mixture worth Rs. 210 per litre. Find the required ratio.

Using alligation:

Ratio=(250-210):(210-150)

=40:60=2:3

Therefore, the required mixing ratio is 2:3.

Number Line Method

The number line method provides a visual way to understand alligation. It uses the inverse relationship between the quantities and their distances from the resultant value.

For example, if two ingredients are mixed in the ratio 7:3, their distances from the resultant value will be in the ratio 3:7.

This method helps understand how the difference between the original values determines the mixing ratio.

Liquid Mixtures and Concentration Formula

Liquid mixture questions generally involve calculating the concentration of a particular component, such as milk, water or alcohol.

Concentration Formula:

Concentration=QuantityofComponentTotalMixture100

For example:

• Milk and water in the ratio 3:1 contain 75% milk.

• Milk and water in the ratio 2:3 contain 40% milk.

After calculating the concentrations, you can apply the weighted average formula or the alligation method to find the resultant concentration.

Example:

Two mixtures contain 75% and 40% milk, respectively. They are mixed in the ratio 2:5. Find the resultant milk concentration.

R=75(2)+40(5)2+5

\[ R=\frac{150+200}{7}=50\% \]

Therefore, the resultant mixture contains 50% milk.

Important Types of Mixture Questions

Different types of mixture questions require different approaches. The following concepts are important for solving such questions.

Mixtures Involving Profit and Loss

Some mixture questions involve selling a mixture at a given price with a specified profit. In such questions, first calculate the cost price of the mixture and then apply alligation.

Cost Price Formula:

CP=SP1+ProfitRate

Here, the profit rate is expressed as a decimal.

Example:

Two varieties of tea cost Rs. 60/kg and Rs. 65/kg. They are mixed to obtain a selling price of Rs. 68.20/kg at 10% profit. Find the mixing ratio.

First, calculate the mixture's cost price.

CP=68.201.10=Rs. 62

Now, apply alligation:

Ratio=(65-62):(62-60)

=3:2

Therefore, the required mixing ratio is 3:2.

Methods and Shortcuts to Solve Mixture Questions

You can use different methods depending on the information given in the question.

Common Mistakes to Avoid

While solving NIMCET Quantitative Aptitude questions on mixtures and alligation, avoid these common mistakes:

• Applying alligation without checking whether the resultant lies between the original values.

• Confusing cost price with selling price in profit or loss questions.

• Using different components, such as milk and alcohol, in the same concentration calculation.

• Forgetting to convert ratios into concentrations when required.

• Ignoring units and total quantities.

• Applying the weighted average formula without considering the actual mixing quantities.

Quick Revision Formulas for Mixtures and Alligation

Revise the following formulas to remember the important concepts covered in this topic.

Understanding concepts and practising different question types can help you strengthen your quantitative aptitude preparation. Along with mixtures and alligation, revise the other topics included in the examination syllabus.

You can explore NIMCET online coaching batches to learn about the available preparation programmes. Also, refer to the NIMCET exam pattern to understand the examination structure and plan your preparation accordingly.