Original Study Notes for Banking, SSC and Railway Exams
These notes are written in simple English for beginners and competitive-exam students. They include basic concepts, formulas, shortcut tricks, step-by-step solved examples, and practice MCQs suitable for classroom teaching, revision notes, and educational websites.
The explanations and examples below are newly written for this material. Basic mathematical formulas and concepts are standard mathematics, so this is not a legal guarantee that every phrase is unique.
Example 1: A class has 20 boys and 15 girls. Find the ratio of boys to girls.
Step 1: Write the quantities.
Boys = 20, Girls = 15
Step 2: Write the ratio.
Step 3: Divide both terms by their HCF, which is 5.
Answer: 4:3
This means that for every 4 boys, there are 3 girls.
Always compare quantities in the same units.
Simplify a ratio by dividing both terms by their HCF.
The order matters: 3:5 is different from 5:3.
A ratio has no unit after the quantities are converted to the same unit.
Example 2: Find the ratio of 2 metres to 50 centimetres.
Example 3: Check whether \(4:6\) and \(10:15\) are in proportion.
Step 1: Multiply the extremes.
Step 2: Multiply the means.
Step 3: Compare both products.
Since 60=60, the ratios are in proportion.
Answer: Yes, 4:6=10:15.
Premium competitive exam preparation institute in Mumbai, helping students achieve their dream careers in Banking, SSC, Railways, Law, and Management.
Copyright © 2026 Aaditya Parmar. All rights reserved. Design & developed by Websitemitra