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Read the posting on **Sarin participates in school anniversary event part 1 **for story on school anniversary.

Read the posting on **Sarin learns concept of ratio in school** to understand Ratio.

Read also the posting on **Sarin learns the concept of Fraction (mathematics concept)** to understand Fraction.

*Challenge yourself with the question before look out for the given solution‼*

**Upper primary school mathematics question UPQ397**

Two classes of pupils were assigned to help up Sarin’s team in the anniversary dinner event. The ratio of the number of pupils in Class Unity to the number of pupils in Class Joyce was 3 : 4 at first. 1/3 of the pupils in Class Unity and 7/12 of those in Class Joyce were boys. In order to have equal number of boys in the two classes, 30 pupils were reshuffed between the two classes. How many pupils were there in each class at first?

Solution:

First draw the model based on the class ratio of 3 : 4

Added the information of the fraction of boys in the each classes

The model

From the model

Assume the 30 pupils reshuffled are boys

2 units = 30

1 unit = 15 pupils

The total number of pupils in Class Unity at first = 9 × 15 = 135

The total number of pupils in Class Joyce at first = 12 × 15 = 180

Alternative solution:

By ratio,

(Boys + Girls ) in Unity : (Boys + Girls) in Joyce = 3 : 4

Boys in Unity : Girls in Unity : all in Unity = 3 × 1/3 : 3 × 2/3 : 3 = 1 : 2 : 3 = 3 : 6 : 9

Boys in Joyce : Girls in Joyce : all in Joyce = 4 × 7 : 4 × 5 : 4 × 12 = 7 : 5 : 12

The different of number of boys in Unity and Joyce in term of units = 7 – 3 = 4 units

To have Boys to be the same in Unity and Joyce

2 units of boys needed shifted from Joyce to Unity

If the 30 pupils moved are all boys

2 units = 30

1 unit = 15 boys

The total number of pupils in Class Unity at first = 9 × 15 = 135

The total number of pupils in Class Joyce at first = 12 × 15 = 180

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