Ratio and proportion

Story hook

It is a sleepy Sunday afternoon. You and your younger sister are sharing a packet of biscuits. But there is a little problem. You are older and hungrier, so your mother says, "Share them so that for every 3 biscuits you take, your sister takes 2."

You count out: 3 for you, 2 for her. Then again: 3 for you, 2 for her. And again. Each time you keep that 3-to-2 pattern.

Notice something lovely. Your mother never told you the exact number of biscuits to take. She did not say "you get 12, she gets 8." She just gave you a pattern of sharing — 3 for every 2 — and that pattern works whether there are 5 biscuits or 50.

That pattern, "3 for every 2," has a special name in maths. We call it a ratio, and we write it as 3 : 2 (read aloud as "three to two").

In this lesson we will learn what a ratio really is, how to make it simpler, how to share any quantity using a ratio, and a magic little helper called the unitary method. We start from absolute zero — no prior knowledge needed. Take a deep breath and let's begin.

Why this matters for UPSC

For your CSAT exam (UPSC Prelims Paper II):

• CSAT is a qualifying paper. That means you do not need a brilliant score — you only need 33% (that is 66 marks out of 200) to pass. Ratio and proportion questions are among the friendliest and most predictable in the whole paper, so they are perfect for safely collecting those qualifying marks.
• Ratios hide inside lots of other topics — mixtures, partnership, speed, profit sharing, and data charts. Once you are comfortable with ratios, several other chapters suddenly feel much easier.

For real life (this is the fun part):

• Cooking uses ratios all the time ("2 cups rice to 3 cups water").
• Maps use a ratio called scale ("1 cm stands for 5 km").
• Sharing money or sweets fairly between friends is pure ratio.
• Mixing paint or squash to get the right colour or taste is a ratio.

So this is not just an exam topic. It is one of the most useful everyday skills in all of maths. And it begins as simply as sharing biscuits with your sister. Stay relaxed and follow each step.