MBA Foundation: Ratio and Proportion

MBA Foundation Batch - Introduction to Ratio & Proportion

• The MBA Foundation Batch aims to teach subjects important for CAT and MBA exams from scratch, focusing on building a strong foundation.
• Ratio & Proportion are crucial due to their direct applications and relevance in Quantitative Aptitude (QA) and Data Interpretation (DI).

Basic Concepts of Ratios

• A ratio is represented as a/b or a:b.
• 'a' is the antecedent, and 'b' is the consequent.
• Knowing these terms is important; questions might use "consequent" instead of "ratio."

Types of Ratios

• Duplicate Ratio: The square of the original ratio (e.g., for 2:5, the duplicate ratio is 4:25).
• Sub-duplicate Ratio: The square root of the original ratio.
• Triplicate Ratio: The cube of the original ratio (a³:b³).
• Sub-triplicate Ratio: The cube root of the original ratio.

Compound Ratio

• The compound ratio of multiple ratios is found by multiplying the corresponding terms of each ratio.
• For ratios a:b, c:d, and e:f, the compound ratio is (a*c*e) : (b*d*f).

Key Rule for Solving Ratio Problems

• Ratios can be multiplied or divided by the same constant without changing the ratio's value for solving equations.
• Addition or subtraction with a constant across the ratio will not work.

Equalizing Ratios to a Common Platform

• Problem: Ratios a:b and b:c are given, requiring a comparison of a, b, and c in a single ratio.
• B is the common link and needs to be equalized.
• Example: a:b = 2:3, b:c = 5:7, equalize B.
• Multiply the ratios to achieve a common multiple for b (in this case, 15).
• All components must be multiplied.

Mirror Image Shortcut

• Mirror image is a better technique for equalizing ratios.
• Given a:b = 2:3 and b:c = 5:7, write the ratios in a column format.
• Copy '3' (from 2:3) to the right and '5' (from 5:7) to the left.
• Multiply vertically: 2*5, 3*5, 3*7 to get the new ratio 10:15:21.

Example Question 1

• If 2a=3b=4c, find a:b:c.
• Assume all are equal to 12 (LCM of 2, 3, and 4), so:
• 2a = 12 => a = 6
• 3b = 12 => b = 4
• 4c = 12 => c = 3
• Result: a:b:c = 6:4:3

Example question 2.

• Given x/2 = y/3 = z/7, find the value of (2x-5y+4z) / (2x+3y-z).
• Since all are equal, assume they are all equal to 1.
• Solve for all variables to find the value:
• x/2 = 1, so x = 2
• y/3 = 1, so y = 3
• z/7 = 1, so z = 7
• Plug the values ​​into the expression.
• The result is 17/6.

Word Based Question Example

• P and Q have an average temperature, and Q and R have an average temperature.
• P:Q is 11:12, and Q:R is 9:8. Find the temperature for Q:R.
• Use the mirror image to resolve and equalize Q.
• Then divide by 4 on both sides.

Applying Ratios to Actual Amounts

• A sum of money (e.g., 1210) needs to be divided in a ratio.
• To solve these questions, take the ratios and divide each amount accordingly.

Fractional Based Ratios

• Questions may provide difficult rational numbers.
• Convert these numbers into linear form by multiplying each side of the fraction to create a common multiple divisible by all numbers.
• Then solve the linear ratios.

Concept of Proportion

• Proportion: Equality of two ratios (a/b = c/d).
• In a proportion, a, b, c, and d are said to be in proportion.
• Cross multiplication is a useful technique: a*d = b*c.

Continuous Proportion

• Continuous Proportion is represented by A/B = B/D.
• Application of cross multiplication for solving.

Assumption Approach

• The assumption approach is very important for difficult questions.
• You can assume general values ​​to all variables if a relationship is provided.

Word Based Proportion Question Example

• "In the famous Bhuj Island, there are 4 men for every 3 women, and 5 children for every 3 men." The ultimate question is how many children are on the island if the population is 531 women.
• Two ratios need to be combined:
  • Men/Women = 4/3
  • Children/Men = 5/3
• Equating them will provide a combined ratio.

Ratios with both known and unknown numbers Example

• Two numbers are in the ratio 5:3.
• A common multiple is used to set the ratio: 5x:3x
• Example ratio to resolve -> 3x + 10/ 5x + 10

Ratios with adding quantity of something

• Mixtures can be represented using ratios.
• Milk and water are provided with equal ratios -> 5:1.
• Consider the ratio of milk to water on adding 5 liters of water.
• Create an equation with milk and water on adding more water.
• Solve for this solution to find the ratio.

CAT/OMET Level Questions - Translating Equations

• Translating equations is an important step.
• For example, if someone gets 3 times the marks in Maths compared to English, it represents a ratio relationship.
• Convert this into a ratio: Maths = 3 * English means Maths / English is 3/1 or a ratio of 3:1.

Alloy Problem -> Solved Using Multiple Linear Equations

• Combine multiple ratio questions using linear equations.

Scoring Problem -> Solved Using Ratio Technique

• Question example: a batsman has a score in a certain ratio.
• Set the problem by setting the previous score = variable x and setting up the current score according to the ratio of x -> then solve.
• Multiple problems in the equation.

Racing Problems -> Solved Using Linear Equations

• Multiple racing problems might require a ratio.
• For example, "Vijay beats in run by 60 " can be used to assign a ratio.
• Combine this ratio with future ratios to find the answer.

Mixture Questions

• Three vessels each of 35L ratio are mixed.
• Use ratios to identify new relationship ratios.