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Ratio Calculation

Ratio Calculation problems involve comparing two or more quantities using ratios. You may need to simplify ratios, find a part given the ratio and total, or solve problems involving ratio relationships.

10Worksheets
200+Practice Questions
BeginnerDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Ratio Calculation

Ratio Calculation problems involve comparing two or more quantities using ratios. You may need to simplify ratios, find a part given the ratio and total, or solve problems involving ratio relationships.

Prerequisites

Ratio concept (a:b means a/b) Fraction simplification Basic arithmetic Proportion concepts
Why This Matters: Ratio problems appear frequently in competitive exams. You can expect 2-3 questions in SSC CGL, 2-3 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Ratio Calculation Problems

1

Step 1: Write the ratio in the form a:b

2

Step 2: Simplify by dividing both terms by their GCD

3

Step 3: To find a part given total, use: part = (ratio term / sum of ratios) × total

4

Step 4: To find total given a part, use: total = (part / ratio term) × sum of ratios

5

Step 5: For two ratios, cross-multiply to compare

6

Step 6: Verify that the parts add up to the total

7

Step 7: Present the answer in simplest ratio form

Pro Strategy: Always find the value of one ratio part first. This makes it easy to find all individual parts and the total.

Example Problem

Example: In a ratio of 3:5, if the first part is 24, find the second part and the total. Solution: Step 1: Ratio = 3:5 Step 2: If first part (3 parts) = 24, then 1 part = 24 ÷ 3 = 8 Step 3: Second part = 5 × 8 = 40 Step 4: Total = 3×8 + 5×8 = 24 + 40 = 64 Answer: Second part = 40, Total = 64

Pro Tips & Tricks

  • a:b means a/b, not b/a
  • Ratios have no units - they are dimensionless
  • To compare ratios a:b and c:d, compare a×d and b×c
  • If a:b = c:d, then a×d = b×c (cross multiplication)
  • The sum of ratio terms represents the total number of parts
  • Ratios can be extended to three or more terms (a:b:c)

Shortcut Methods to Solve Faster

Value of one part = Total ÷ Sum of ratio terms
Individual part = Ratio term × (Total ÷ Sum of ratios)
If a:b and b:c are given, combined ratio = a:b:c = (a×LCM):LCM:(c×LCM/b)

Common Mistakes to Avoid

Reversing the ratio order (confusing a:b with b:a)
Not simplifying ratios before calculation
Using ratio terms directly as actual values
Forgetting that ratio terms are proportional, not absolute

Exam Importance

Ratio Calculation is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
2-3 questions
INSURANCE
2-3 questions

Ready to Master Ratio Calculation?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now