Learn this concept that can help score AL1 in Math PSLE (Shortage and Excess)

Not all hard problem sums are fractions. Here is an example of a problem sum that is hard, but not a fraction problem sum:

Mrs Tan gave some sweets to a group of children. If she gave 15 sweets to each child, there would be a shortage of 10 sweets. If she gave 10 sweets to each child, there would be 30 sweets left. How many children are there in the group?

Not that easy, right? Don't worry. I'm here to share with you how to solve this kind of question called the Shortage and Excess question.

What Are Shortage & Excess Concept Problems?

These problems involve two different giving situations with opposite outcomes:

• In one situation, there is a shortage (not enough).
• In the other, there is an excess (too much / left over).

For example:

• If she gives 15 sweets each → she is short of 10 sweets
• If she gives 10 sweets each → she has 30 sweets left

This is the classic structure of this concept.

How to Spot a Shortage & Excess Question

Look out for these signs:

✔ Two different “if” situations
✔ Words like “short”, “shortage”, “lack”, “excess”, “left”, “remaining”
✔ You know the number of items (sweets, pencils, etc.)
✔ You don’t know the number of people

Once you identify these features, congratulations — you’ve spotted a Shortage & Excess problem.

Example Problem

Mrs Tan gave some sweets to a group of children. If she gave 15 sweets each, she would be short of 10 sweets. If she gave 10 sweets each, she would have 30 sweets left. How many children are there?

Let’s apply the 3-step method.

Step-by-Step Solution

Step 1: Let 1u = total number of children

We choose this because the number of children is the unknown we want to find.

Step 2: Form equations using both situations

Situation 1: Give 15 sweets each → shortage of 10
Total sweets = 15u – 10
We subtract 10 because she is short by 10.

Situation 2: Give 10 sweets each → 30 left
Total sweets = 10u + 30
We add 30 because she has 30 sweet left (excess).

Step 3: Set the two equations equal

Both expressions represent the SAME total number of sweets.

So we set them equal:

15u – 10 = 10u + 30
5u = 40
u = 40 ÷ 5
u = 8

Answer: There are 8 children.

Final Tips

✔ Look for 2 situations
✔ Spot keywords: shortage, left, remaining, excess
✔ Let 1u = number of people
✔ Form both equations carefully
✔ Set them equal and solve

Master this concept, and you or your child will stop guessing and start solving with confidence. 😊