# 4 Must Know Concepts of Ratio Math Problems

PSLE Ratio Math problems consist of many marks in the exam and you cannot afford to lose them.

No matter how the questions twist and turn, here are 4 PSLE Ratio concepts which the questions will test. For more concepts, check out this post on the 8 Must Know Methods for PSLE Math.

## 1. Constant Part

Constant part means one of the parts remained the same while the other part changed.

In this case, you will need to make the part which remained the same to be equal to each other.

Example: *Ali and Billy have money in the ratio of 5 : 6. After Billy spent $16, the ratio became 3 : 2. How much money does Billy have in the end?*

Before:

A : B

= 5 : 6

= 15 : 18

After:

A : B

= 3: 2

= 15 : 10

18u – 10u = 8u

8u = $16

1u = $2

10u = **$20 (Ans)**

## 2. Constant Total

Constant Total means the total remained the same. Usually, this concept applies for question related to “Internal Transfer”.

If A transfer an amount to B, A will decrease while B will increase by the same amount. So the total will stay the same.

Example: *Ali and Billy have money in the ratio of 5 : 4. After Ali gave Billy $20, they have an equal amount of money. How much money does Billy have in the end?*

Before:

A : B : Total

= 5 : 4 : 9

= 10 : 8 : 18

After:

A : B : Total

= 1 : 1 : 2

= 9 : 9 : 18

1 unit = $20

9 units = **$180 (Ans)**

## 3. Constant Difference

Constant Difference means the difference remained the same. Usually, this concept applies for question related to “Age”.

As years go by, the age difference between 2 people will always be the same, because both will grow old together.

Example: *The ages of Ali and Billy are in the ratio of 4 : 7. In 3 years time, their ages will be in the ratio of 3 : 5. How old is Billy now?*

Before:

A : B : Difference

= 4 : 7 : 3

= 8 : 14 : 6

After:

A : B : Difference

= 3 : 5 : 2

= 9 : 15 : 6

1 unit = 3 years

14 units = **42 years old (Ans)**

## 4. Everything Changed

As the name says, everything changed! Every part changed, the difference changed, the total changed… Nothing remained the same.

This type of questions are usually the last few 5 marks questions in the paper. So make sure you know how to do this type of questions.

There are a few methods to solve this type of question. I will use an example below to show a method which you can use.

Example: *The ratio of Ali’s money to Billy’s money was 2 : 1. After Ali saved another $60 and Billy spent $150, the ratio became 4 : 1. How much money did Ali have at first?*

Step 1: Write down the starting ratio and apply the changes.

Step 2: Compare the final units with the final ratio.

A : B

= 2u + 60 : 1u – 150

= 4 : 1

Step 3: Cross Multiply the final units with the final ratio

1 × (2u + 60) = 4 × (1u – 150)

2u + 60 = 4u – 600

Step 4: Solve for 1 unit

2 units = 60 + 600 = **$660 (Ans)**

These are the 4 must-know concepts of PSLE Ratio Math problems. Make sure you know when to apply the concept and how to use them correctly.

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