Solving problem sums involving quantity, percentage and changes to the quantity

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. Expresses the quantity of one item as a percentage of another item

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

4. The new percentage 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, 60% of the students are girls while the rest are boys. After 15 boys left the class, only 10% of the students are boys. What is the total number of students in the class at first?

Breaking Down the Example Problem

• The persons/objects involved: 

  • Girls (G)

  • Boys (B)

• The starting info: 

  • G : B = 60% : 40%

• Change that happened: 15 boys left

• The ending info:

  • G : B = 90% : 10%

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

General Technique To Use

You can follow the following steps to solve such problems:

1. Express the percentage as ratio (use your calculator reduce it to the lowest ratio)

2. Apply the “Problem Sum: Ratio of Quantity that Changed (Before-After)” technique to solve it!

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

Change the percentage into ratio: 

• 60% of the students are girls while the rest are boys => Ratio of Girls to Boys = 60 : 40 = 3 : 2

• Only 10% of the students are boys => The ratio of Girls to Boys = 90 : 10 = 9 : 1

More Similar Problems

1. In a class, 60% of the students are girls while the rest are boys. After 9 boys joined the class, there are equal number of boys and girls. 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. The number of sweets Alicia has is 40% that of Betty's. After Betty gave Alicia 18 sweets, Alicia had as many sweets as Betty. How many sweets did Alicia have initially? (Hint: The total is unchanged)

   Ans: Alicia had 24 sweets initially

3. The number of sweets Charles had was 75% that of David. Elias decided to give both Charles and David 12 sweets each. After receiving the sweets from Elias, Charles had 45% of the total number of sweets. 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