Independent School Entrance (ISEB Pre-Test and 11+ CEM style) · Numerical Reasoning

Word problems and rates

20 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 20 questions

  1. A shop's takings from Monday to Friday were £420, £385, £510, £465 and £390. The shop wants the mean daily takings for the week to reach £450. How much more would it need to have taken in total?
  2. 300 ml of squash that is 20% concentrate is mixed with 200 ml of squash that is 45% concentrate. What percentage of the mixture is concentrate?
  3. A tank holds 280 litres. A tap fills it at 12 litres per minute, but a drain at the bottom empties it at 5 litres per minute. Both are on and the tank starts empty. How long does it take to fill?
  4. A machine only gives stamps worth 3p and 5p. What is the largest amount that CANNOT be made exactly using these stamps?
  5. Ali cycles at 12 km/h starting at 09:00. Beth leaves the same place at 10:00 on the same route at 20 km/h. At what time does Beth catch Ali?
  6. A room is 3.6 m long and 2.4 m wide. It is covered with square tiles of side 30 cm, with none cut. How many tiles are needed?
  7. A mother is three times as old as her daughter. In 12 years' time she will be twice as old as her daughter. How old will the mother be in 12 years' time?
  8. A car uses 6.5 litres of petrol per 100 km and has a 52-litre tank. How far can it travel on a full tank?
  9. Six painters could paint a building in 10 days. After 4 days, 2 painters leave. The remaining painters work at the same rate. How many days in total does the job take?
  10. A bus leaves a station every 18 minutes and a train every 24 minutes. Both leave at 08:00. At what time do they next leave together?
  11. To change °C to °F, multiply by 9/5 and then add 32. What is 35°C in °F?
  12. Plan A costs £12 a month plus 5p per minute. Plan B costs £20 a month and includes 100 minutes, then charges 8p per minute. How much cheaper is Plan A than Plan B for 250 minutes in a month?
  13. Four friends share a taxi fare of £28 equally. They also add a 15% tip to the fare. How much does each friend pay?
  14. An orchard has 12 rows of 15 trees. Every fifth tree is a pear tree and all the others are apple trees. How many apple trees are there?
  15. A library charges nothing for the first 3 days that a book is overdue, then 15p for each further day. How much is the fine for a book that is 12 days overdue?
  16. A photograph measures 12 cm by 8 cm. It is enlarged so that the width of 12 cm becomes 30 cm, keeping the same shape. What is the new height?
  17. A runner's four lap times were 1 min 12.4 s, 1 min 10.9 s, 1 min 11.6 s and 1 min 9.5 s. What was the mean lap time?
  18. A jacket costs £120. A shop takes 25% off, and then takes a further 10% off the reduced price. How much MORE does the jacket cost than if a single reduction of 35% had been given?
  19. Zoe saves £15 in week 1 and each week after that she saves £5 more than the week before. After how many weeks will her total savings first reach at least £500?
  20. A 25 m rope is cut into as many pieces of 1.6 m as possible. How much rope is left over?

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