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Arithmetical Reasoning: Turn the Story into One Equation
Arithmetical reasoning questions hide simple arithmetic inside a short story: a purse of coins, a farm of hens and goats, a hall of people shaking hands. Students panic because the story is long, yet almost every question rests on one idea: total = (number of items) × (value of each item), added over the groups. Two habits solve most of them. First, write down what is being counted and what the total measures, for example heads versus legs, or coins versus rupees. Second, use the assumption method: pretend everything belongs to one group, see how far the total is off, and correct it one item at a time. This short covers the assumption method for coins, notes and legs, and the counting formulas for handshakes, matches and trees. Once the pattern is known, each question takes about a minute.
1. A purse has 50 coins of ₹1 and ₹5 worth ₹130 in all. How many ₹5 coins are there?
2. A yard has hens and goats with 35 heads and 94 legs in all. How many goats are there?
3. At a meeting 12 people each shake hands once with every other person. How many handshakes take place?
4. A knockout tournament starts with 32 teams. How many matches are needed to decide the champion?
5. Trees are planted every 10 m along a straight 100 m road, with a tree at both ends. How many trees are planted?
6. A cashier has 35 notes of ₹10 and ₹20 worth ₹550 in all. How many ₹20 notes are there?
7. In a league of 8 teams every team plays every other team exactly once. How many matches are played?
8. Trees are planted every 5 m around a circular park whose boundary is 100 m long. How many trees are needed?