Free 11+ maths practice question: Ratio of counters changes
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A box holds red and blue counters in the ratio 2 : 5. When 6 more red counters are put in, the ratio of red to blue becomes 1 : 2.
How many counters are in the box now?
THE COUNTERS
At the start, red : blue2 : 5
Added6 red counters
Now, red : blue1 : 2
💡 Hints
When a ratio changes because something is added
Write the starting amounts as equal parts, such as 2 parts and 5 parts. Only the colour that is added to changes.
The new ratio is a fact about the new amounts, so turn it into a sentence: one is double the other, or three times it.
Solve for one part, then read the question again — it may want a total, and the added counters belong in it.
Sweets are red : green = 3 : 4, and after 5 more red the ratio is 1 : 1, so one part is 5, there were 15 red and 20 green, and the total now is ?
🗝️ Key method: work in parts
Write red and blue as 2 parts and 5 parts.
After the 6 red, blue must be double red.
Find one part, then total everything.
1
Let one part be p, so the box starts with 2p red counters and 5p blue counters.
2
After 6 red counters go in there are 2p + 6 red, and the new ratio says blue is double that: 5p = 2(2p + 6).
3
So 5p = 4p + 12, giving p = 12: the box started with 24 red and 60 blue counters.
4
Now there are 24 + 6 = 30 red and 60 blue, which is 90 counters altogether.
🎉 Answer: E. 90
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