Solving problem sums involving a ratio that is changed with an action

An example from our high quality Primary Mathematics Tuition

How To Identify Such Problems

Such problems will typically have all of the following:

1. Involves 2 items

2. An initial ratio between the 2 items is given

3. An action increases or decreases one or both of the items.

4. The new ratio after the action is given

5. Need to solve for the quantity of a specific item

*Don’t worry if you don’t fully understand above at this point. Use the following example to help you with your understanding. Come back here again after you have gone through the rest of the tip.

An Example Problem

In a class, the ratio of the number of girls to the number of boys is 3 : 2. After 15 boys left the class, the ratio of the number of girls to the number of boys became 9 : 1. What is the total number of students in the class at first? 

Breaking Down the Example Problem

• The persons/objects involved: 

  • Boys (A)

  • Girls (G)

• The starting ratio: 

  • G : B = 3 : 2

• Change that happened: 15 boys left

• The ending ratio: 

  • G : B = 9 : 1

• Problem to solve: Total number of students initially = ? 

General Technique To Use

You can follow the following steps to solve such problems:

1. Clearly write down the starting and ending ratios

2. Identify the quantity that did not change. The unchanged quantity could be one of the following

   • One of the items

   • Total quantity

   • The difference

3. Adjust the two ratios so that the numbers for item that did not change is the same in both ratios

4. Use the change information to calculate the value for a ratio unit

5. Solve the question

*Don’t worry if you don’t fully understand the above. Use the following example to help you with your understanding. Come back here again after you have gone through the step-by-step solution of the example problem.

Solving the Example Problem (Step-By-Step Guide)

More Similar Problems

1. In a class, the ratio of the number of girls to the number of boys is 3 : 2. After 9 boys joined the class, the ratio of the number of girls to the number of boys became 1 : 1. What is the total number of students in the class at the beginning? (Hint: This is a slight variation from the example problem) 

   Ans: Total of 45 students initially

2. Alicia and Betty had a number of sweets in the ratio of 2 : 5. After Betty gave Alicia 18 sweets, the ratio of the number of sweets Alicia and Betty have is 1 : 1. How many sweets did Alicia have initially? (Hint: The total is unchanged)

   Ans: Alicia had 24 sweets initially

3. Charles and David had a number of sweets in the ratio of 3 : 4. Elias decided to give both Charles and David 12 sweets each. After receiving the sweets from Elias, the number of sweets Charles and David have are in the ratio of 9 : 11. How many sweets did David have initially? (Hint: The difference in the number of sweets between Charles and David is unchanged)

   Ans: David had 32 sweets initially