Mixtures and alligation

Story hook

Picture a small tea shop on a busy morning. The shopkeeper, Ravi uncle, has two tins of tea leaves. One tin is a cheap tea costing 200 rupees per kilogram. The other is a fancy tea costing 300 rupees per kilogram.

Ravi uncle wants to sell a nice "house blend" — a mix of the two — and he plans to charge 240 rupees per kilogram for it. A young customer, Meera, watches him scoop leaves from each tin and asks, "Uncle, how do you know how much of each tea to put in so the mix costs exactly 240?"

Ravi uncle smiles. "There is a little trick for that. It tells me the ratio — how many scoops of the cheap tea for every scoop of the costly one — so the price comes out just right."

That little trick is called alligation (don't worry about the funny name — we will explain it fully). It is one of the neatest, fastest tools in the whole maths paper. By the end of this lesson you will be able to mix two teas, two kinds of rice, or even water into juice, and find the exact right ratio in your head. Let's start from zero — no maths needed yet.

Why this matters for UPSC

For your CSAT exam (UPSC Prelims Paper II):

• CSAT is a qualifying paper. You do not need a brilliant score — you only need 33% (that is 66 marks out of 200) to pass. Mixtures and alligation questions look scary because of the name, but they are actually among the fastest sums once you know the cross trick. A question that takes others two minutes can take you twenty seconds.
• This topic is really just averages and ratios wearing a costume. So every minute you spend here also strengthens two other big topics. Good value for your time.

For real life (this is the fun part):

• Shopkeepers blend tea, coffee, spices and rice to hit a target price — exactly Ravi uncle's problem.
• You dilute squash or juice with water to make it go further (and taste right).
• You mix petrol grades, paints, or two kinds of flour and want to know the cost or the proportion.
• Anyone splitting a shared cost where some paid more and some paid less is quietly using the same idea.

So this is not just an exam trick — it is the everyday skill of mixing two things of different value and knowing exactly what comes out. Stay relaxed; it starts as simply as making a glass of squash.