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Average looks like the easiest topic in the arithmetic section, and that is exactly why it costs marks. The formula — sum divided by count — is learnt in class six, so nobody revises it, and then a question arrives that gives you the average instead of the sum and expects you to work backwards.
Two ideas fix almost every average question you will ever see. First, an average is just a total in disguise: if eleven players average 25 years, their ages total 275 years, and that total is the number you actually calculate with. Second, when two groups with different averages are mixed, the mixed average always lands between them, closer to the bigger group — and alligation is simply the shortcut that tells you how much closer. Master those two, and the whole chapter, including mixtures and replacement, collapses into arithmetic you can do in your head.
1. What is the average of the first 20 natural numbers?
2. A man travels from A to B at 60 km/h and returns at 40 km/h. His average speed for the whole journey is:
3. A batsman has an average of 45 runs in 15 innings. He scores 65 in his sixteenth innings. His new average is:
4. The average weight of 8 people increases by 2.5 kg when a person weighing 65 kg is replaced by a new person. The weight of the new person is:
5. In what ratio must rice costing ₹30 per kg be mixed with rice costing ₹45 per kg so that the mixture costs ₹35 per kg?
6. From a vessel containing 40 litres of pure milk, 4 litres are drawn out and replaced with water. This is done three times in all. The quantity of milk left is:
7. In a class, 30 boys have an average of 60 marks and 20 girls have an average of 70 marks. The average marks of the whole class is:
8. The average of the first n odd natural numbers is: