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Primary 6 · Ratio · Question type 1.11

P6 Ratio: Ratio Questions Where Neither Quantity Stays the Same

Divide the units so each fractional change becomes a whole number of smaller units.

Try the question yourself, or watch the lesson first.

Primary 6, on the MOE Primary Mathematics syllabus.

In the Ratio chapter10 question types · see the chapter

The lesson · 3 minutes 36 seconds

How do you solve P6 ratio questions when neither quantity stays the same?

Watch: roses and tulips sold, and nothing stays the same

Another worked example

A worked example

A florist had roses and tulips. The number of roses to the number of tulips was 3 : 2. 2/9 of the roses and 1/4 of the tulips were then sold. After that, there were 55 more roses than tulips left. How many roses did the florist have at first?

The working · Seven lines

The step-by-step working

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

  1. roses : tulips = 18 : 12
  2. roses: 2/9 × 18 = 4 units sold
  3. tulips: 1/4 × 12 = 3 units sold
  4. roses left: 18 - 4 = 14 units tulips left: 12 - 3 = 9 units
  5. difference: 14 units - 9 units = 5 units
  6. 5 units = 55, 1 unit = 55 ÷ 5 = 11
  7. 18 units = 18 × 11 = 198 roses

The florist had 198 roses at first.

Practise · Modelled on top school exam questions

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Find the cookies at first

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A tin held almond cookies and chocolate cookies in the ratio 3 : 4. 35 of the almond cookies and 60% of the chocolate cookies were then eaten. After that there were 7 more almond cookies than chocolate cookies left. How many cookies were in the tin at first?

Show the step-by-step solution
  1. almond : chocolate = 3 : 4
  2. 60% is taken off the chocolate, so the chocolate must divide into fifths
  3. the chocolate reads 4, and it has to reach a multiple of 5: 4 × 5 = 20
  4. almond : chocolate = 3 : 4
  5. × 5 = 15 : 20
  6. chocolate eaten = 60% of 20 units = 12 units
  7. chocolate left = 20 units - 12 units = 8 units
  8. almond left = 15 units - 35
  9. almond left is 7 more than chocolate left
  10. 15 units - 35 - 8 units = 7
  11. 7 units = 7 + 35 = 42
  12. 1 unit = 42 ÷ 7 = 6
  13. 35 units = 35 × 6 = 210 cookies

Ans: 210

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