In a container, the ratio of the number of chocolate cookies to butter cookies was 1:3.
After 24 butter cookies were removed and replaced with 24 chocolate cookies, the ratio of chocolate cookies to butter cookies became 7:5.
How many chocolate cookies were in the container at first?
Your child will face plenty of problem sums like these across school worksheets, class tests, and the PSLE itself. Here’s how to solve PSLE problem sums step by step; though some problem sums will require more steps and have different approaches from others.
Step 1: Deconstruction
Deconstruction means breaking down a block of text, sentence by sentence, into simple mathematical clues. Instead of trying to read the entire story at once, your child pulls out key information piece by piece.
Applying it to our cookie question, your child records the following notes:
- Clue 1: Chocolate-to-butter cookies start at a 1:3 ratio.
- Clue 2: 24 butter cookies leave, and 24 chocolate cookies enter.
- Clue 3: The final ratio changes to 7:5.
By comparing these clues, your child spots the key insight. Since 24 items left and exactly 24 items entered, the total cookie count inside the container stayed the same. The ratio of the types of items, however, did.
Step 2: List the Ratios and Calculate the Totals
Once your child finishes pulling out the clues, they need to write down the before-and-after states side by side and find the sum of their units. This is one of the more useful PSLE math tips students must adopt, as it helps with a range of other problem sums.
This step tracks how the overall quantity changes over time.
For our cookie problem, we write the mathematical units out like this:
- Before State: Chocolate:Butter = 1:3
- Total Units Before = 1 + 3 = 4 units
- After State: Chocolate:Butter = 7:5
- Total Units After = 7 + 5 = 12 units
Step 3: Equalise the Total Units
Equalising total units means scaling the ratios using the lowest common multiple so that the unchanged values match up perfectly.
Since the deconstruction step showed that the overall cookie count remained constant, the total units in both ratios must be identical.
Looking at the list from the previous step, the totals are 4 units and 12 units.
The lowest common multiple of 4 and 12 is 12. To scale the Before total to 12, multiply the entire before ratio by 3:
Before State (Scaled) = (1 x 3) : (3 x 3) ➡ 3 : 9
Now you have a shared scale to compare both states directly:
- Before: 3:9 (Total = 12 units)
- After: 7:5 (Total = 12 units)
Step 4: Find the Value of 1 Unit
Finding the value of 1 unit involves examining the change in scaled units and comparing it to the real numbers provided in the text.
This gives an exact numerical value to a single unit.
With the scaled values from the previous step, you can see the change in chocolate cookies: they increased from 3 to 7 units. That is an increase of 4 units (7 – 3 = 4).
This increase happened because 24 chocolate cookies were added to the container.
You can now solve for a single unit:
4 units = 24 cookies
1 unit = 24 / 4 = 6 cookies
So a single unit represents six cookies.
Step 5: Calculate the Final Target
Calculating the final target means taking the value of 1 unit and multiplying it by the number of units requested in the final question sentence.
The question asks for the number of chocolate cookies in the container at first. Referencing your scaled ‘Before’ ratio, you know chocolate started with 3 units.
Using the unit value found in the previous step, you complete the calculation:
Chocolate cookies at first = 3 units
Chocolate cookies at first ➡ 3 x 6 = 18
Your child can confidently write down 18 as the final answer.
Step 6: Finalising The Answer
To verify this answer, we can reapply it to the problem:
In a container, the ratio of the number of chocolate cookies to butter cookies was 1:3. Now that we know that there were 18 chocolate cookies at first, we can say that 1 unit is equal to 18, and that the exact cookie count was 18 chocolate cookies and 54 butter cookies.
After 24 butter cookies were removed and replaced with 24 chocolate cookies, the ratio of chocolate cookies to butter cookies became 7:5.
Hence, the cookie count after this change became 52 chocolate cookies and 30 butter cookies. This matches the ‘After’ ratio of 7:5.
Types of Ratio Problem Sums Students Should Grasp
To help your child understand how to solve PSLE problem sums, you must guide them to recognise that most ratio questions fall into three core categories. Here are the main variations to focus on during your revision:
Constant Total (Internal Transfer)
This matches the cookie example solved above.
It happens when items move around within the same group, or when equal amounts are swapped simultaneously.
Because nothing truly enters or leaves the entire system, the total number of units remains the same before and after the change.
Constant Part (One-Object Changed)
This type occurs when an action only affects one item while the other item remains entirely untouched.
For example, if more boys join a classroom but the number of girls remains the same, the number of girls is constant. Your child must equalise the unchanged item’s units across both ratios.
Constant Difference (Age / Equal Change)
This scenario happens when both groups increase or decrease by the exact same amount.
Common examples include age problems or situations where two people spend the same amount of money.
Since both numbers change equally, the subtraction difference between the two quantities never alters. Your child must equalise the unit difference between both sides.
Enrol in a PSLE Math Tuition Centre for Focused Learning Today
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At The Heuristic Way Tuition, we avoid large, crowded classrooms. Our small group math tuition sets a limit of 10 students per session, ensuring your child receives personal and tailored guidance.
We do not provide generic, one-size-fits-all worksheets. Instead, every student receives customised lesson materials tailored to their personal learning pace and immediate conceptual gaps. Contact us to book a free trial lesson at our Bukit Batok centre today.
Frequently Asked Questions
What should my child do if a ratio problem has three variables instead of two?
Three-variable ratios (e.g., A:B:C = 2:3:5) follow the exact same constant logic. Your child simply needs to identify which structural element remains unchanged, whether it is a single person’s share, the total of all three, or the difference between two specific parties. Once that specific anchor is identified, they scale the entire three-part ratio system using the lowest common multiple, just like a two-variable problem.
If a question asks for a ratio as the final answer, does it matter if it isn’t simplified?
Yes, it matters immensely. If the math yields a final relationship of 6:12, leaving it in that state will result in the loss of the final Accuracy (A1) mark. All final ratios written on the answer line must be reduced to their lowest possible terms using their highest common factor (simplifying 6:12 down to 1:2).
Can ratio problem sums be solved by drawing model bars instead of writing down ratio numbers?
Yes. Model drawing and ratio notation are completely interchangeable expressions of the same mathematical concept. A ratio of 1:3 translates directly into 1 model box stacked next to 3 identical model boxes. While models are excellent for visual learners, ratio notation is often faster for multi-step scaling because it requires less drawing time during the exam.