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Word problems by reasoning – practice for Years 5–7

Sample questions on Word problems by reasoning with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 5–7
Curriculum area
Problem solving and non-routine tasks

Question types: Two unknowns: what if they were all…

Rule: Word problems by reasoning

Imagine they are all of the same kind: “If they were all hens…”

Divide the difference from the real total by how much one of the other kind differs.

Example: 10 hens and rabbits, 28 legs: all hens would have 20 legs, 8 extra ÷ 2 = 4 rabbits

Watch out: At the end check both facts: 6 hens and 4 rabbits have 10 heads and 28 legs.

Sample questions

  1. Question 1 Easy

    Exercise books are sold in packs of 2 and packs of 5. A school bought 8 packs with 22 exercise books in them altogether. How many packs of 5 did the school buy?

    1. A) 1
    2. B) 2
    3. C) 3
    4. D) 4
    5. E) 6
    Show the solution
    Answer: B) 2

    How it works: If all the packs were packs of 2, there would be 8 × 2 = 16 exercise books. There are 22, so 6 more. Each pack of 5 holds 3 more, so there are 6 ÷ 3 = 2 packs of 5 and 8 − 2 = 6 packs of 2.

  2. Question 2 Normal

    Exercise books are sold in packs of 5 and packs of 8. A school bought 15 packs with 81 exercise books in them altogether. How many packs of 8 did the school buy?

    Show the solution
    Answer: 2

    How it works: If all the packs were packs of 5, there would be 15 × 5 = 75 exercise books. There are 81, so 6 more. Each pack of 8 holds 3 more, so there are 6 ÷ 3 = 2 packs of 8 and 15 − 2 = 13 packs of 5.

  3. Question 3 Hard

    Exercise books are sold in packs of 6 and packs of 15. A school bought 22 packs with 159 exercise books in them altogether. How many packs of 15 did the school buy?

    Show the solution
    Answer: 3

    How it works: If all the packs were packs of 6, there would be 22 × 6 = 132 exercise books. There are 159, so 27 more. Each pack of 15 holds 9 more, so there are 27 ÷ 9 = 3 packs of 15 and 22 − 3 = 19 packs of 6.

Related topics

All Maths topics

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