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Primary 6 · Ratio · Question type 1.6

P6 Ratio: Constant Difference Questions

When the same amount is added to both quantities or removed from both, the difference stays unchanged. In a constant difference problem, match the difference in units before and after.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Ratio chapter10 question types · see the chapter

The lesson · 1 minute 51 seconds

How do you solve P6 ratio questions with a constant difference?

Watch: twelve years pass and the difference stays the same

Another worked example

A worked example

A father is 4 times as old as his son. In 12 years' time, he will be twice as old as his son. How old is the son now?

The working · Five lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. difference = 4 units - 1 unit = 3 units
  2. later, difference = 1 new block = 3 units
  3. 2 units = 12
  4. 1 unit = 12 ÷ 2 = 6
  5. 24 + 12 = 36 and 6 + 12 = 18

The son is 6 years old now.

Practise · Modelled on top school exam questions

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Find the books removed

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Shelf A held 138 books and Shelf B held 94 books. The same number of books was taken from each shelf. The number of books left on Shelf A was then 5/3 of the number of books left on Shelf B. How many books were taken from the two shelves altogether?

Show the step-by-step solution
  1. difference at first = 138 - 94 = 44
  2. the same number came off each shelf, so the difference is still 44
  3. 5/3 of Shelf B is 5 units against Shelf B's 3 units
  4. in the end, Shelf A : Shelf B = 5 : 3
  5. 5 units - 3 units = 2 units
  6. 2 units = 44
  7. 1 unit = 44 ÷ 2 = 22
  8. Shelf B in the end = 3 × 22 = 66
  9. taken from Shelf B = 94 - 66 = 28
  10. the same 28 came off Shelf A
  11. taken altogether = 2 × 28 = 56 books

Ans: 56

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