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Ruiya Math Blog · No. 2

A hard PSLE Maths problem: the ratio-and-transfer strategy

A difficult question can feel like three puzzles at once. The calm way through is to make one model, follow exactly what changes, and let the final condition tell you the size of one unit.

An original five-star PSLE-style ratio problem for Primary 6 learners

Why this feels hard

Two ratios share a middle friend — and then the numbers move.

You cannot simply place the two ratios side by side. First, make the shared quantity match. Then treat the transfer like moving books from one shelf to another: one shelf goes up, one goes down, and the third shelf stays exactly where it is.

The one idea to carry with you

A transfer does not change the total. It changes the gap.

So ask: which gap is the question quietly asking me to close?

The original challenge

The recycling-drive token problem

At a school recycling drive, the Orchid, Coral and Fern teams collected tokens.

  • • Orchid : Coral = 3 : 5
  • • Coral : Fern = 4 : 3
  • 24 tokens are moved from Coral to Orchid.
  • After the move, Orchid has the same number of tokens as Fern.

How many tokens did all three teams collect at first?

This is a Ruiya-original PSLE-style practice problem, not a past-paper question.

Strategy 1: build one language

Make Coral mean the same amount in both ratios.

Think of Coral as a measuring cup. In the first ratio, Coral is 5 cups. In the second, Coral is 4 cups. We need one cup size that works for both, so we make Coral 20 units.

Orchid : Coral = 3 : 5

Multiply each part by 4: 12 : 20

Coral : Fern = 4 : 3

Multiply each part by 5: 20 : 15

One joined ratio

Orchid : Coral : Fern = 12 : 20 : 15

Strategy 2: follow the movement

The 24 tokens close a 3-unit gap.

1
Look at the starting gap. Orchid has 12 units while Fern has 15 units. Fern is ahead by 3 units.
2
Read the direction carefully. 24 tokens move to Orchid, so Orchid grows. Fern does not change at all.
3
Use the final equality. Orchid catches Fern exactly, so 3 units = 24 tokens. Therefore 1 unit = 8 tokens.
A ratio bar model for the recycling-drive problemBefore the transfer, Orchid has 12 equal units and Fern has 15 equal units. A highlighted gap of 3 units equals 24 tokens after Coral transfers 24 tokens to Orchid.OrchidFern3 units = 24 tokensAfter 24 move to Orchid:Orchid = Fern = 120 tokens

Finish and check

Now the calculation is small because the thinking is organised.

  1. One unit = 8 tokens. So the original amounts were Orchid 12 × 8 = 96, Coral 20 × 8 = 160, and Fern 15 × 8 = 120.
  2. Find the original total: 96 + 160 + 120 = 376 tokens.
  3. Check the story: move 24 from Coral to Orchid. Orchid becomes 120, Coral becomes 136, and Fern stays 120. The final equality is true.

Traps to watch for

The question is hard because it invites hurried shortcuts.

01

Joining ratios too quickly

3 : 5 and 4 : 3 do not make 3 : 5 : 3. The shared Coral part must be the same size first.

02

Changing the wrong team

Only Coral and Orchid change. Fern is your steady reference point.

03

Treating 24 as the total

The 24 represents the gap of 3 units, not all 47 units in the joined ratio.

04

Forgetting when the fact is true

‘At first’ describes the ratio. ‘After the move’ describes the equality. Keep those moments separate.

How examiners vary the story

The surface changes. The strategy stays.

An examiner may use marbles, money, books, water or people instead of tokens. They may reverse the transfer, ask for one group instead of the total, or say two groups are equal only after a donation. Do not hunt for familiar words. Hunt for the same structure: linked ratios + a movement + a final relationship.

Try a variation

At another drive, Amber : Blue = 4 : 7 and Blue : Clover = 3 : 2. Thirty items are moved from Blue to Amber. Amber then has the same number of items as Clover. How many items were there at first?

Start by making Blue equal in both ratios. Then ask how many units Amber needs to catch Clover. Do not scroll for a shortcut — make the model yourself.

Why this matters outside an exam

Real-life planning often means tracking a changing balance.

A warehouse may divide supplies between three sites in agreed proportions, then move a delivery from one site to another. A school event may rebalance equipment between groups. The names are different, but the useful questions are the same: what was the starting relationship, what moved, what stayed still, and what condition is true now?

That is why a bar model is more than an exam trick. It is a tidy way to keep a changing situation honest.

Try it with Ruiya

Got a hard ratio question of your own?

Send it to Ruiya and ask: “Which quantity should I make equal first?” Start with the model, then let each step earn its place.

Try 20 Free Turns