Arithmetic Word Problems
What you must understand
These questions dress simple arithmetic in words: sharing costs, ages, mixtures of quantities, ticket totals, remaining balances, and multi-step shopping. The arithmetic is easy; the difficulty is translation. Candidates must identify the unknown, assign it a letter or a unit, and convert each sentence into an equation or a single ordered calculation.
Method
Read the whole question before calculating. Underline quantities with units and the relationship words: total, each, remaining, more than, less than, times as many. Work in a consistent unit. For multi-step problems, keep a running note of what each intermediate number represents so you do not add a rate to a total.
Traps
- Percentages and fractions of different bases being combined incorrectly.
- 'Times as many' versus 'more than' - these are not the same.
- Leftover amounts: subtract before dividing, not after.
- Rounding too early in a chain of operations; carry full precision and round only the final answer.
- Answering the intermediate value rather than the quantity asked for.
Worked example
A group of 7 friends splits a restaurant bill equally and each pays €24. One friend later joins and the group agrees to split the same bill equally among all 8. How much does each now pay? Total bill = 7 × €24 = €168. New share = €168 ÷ 8 = €21. The trap is to subtract €24 ÷ 8 from €24; the correct base is the total bill, not the old share.