Percentage · find whole from difference

P6 · Percentage · PSLE Maths

Question

At a P6 school camp, 35% of the pupils were boys. There were 126 more girls than boys. How many pupils were there at the camp altogether?

First think: if boys are 35%, what percentage are girls? What percentage is the difference?

Show the answer and step-by-step explanation

Answer: Total number of pupils at the camp 420 pupils

Draw percent bars — Boys are 35%. The whole is 100%, so girls are 65%. Let 5% be 1 unit: 35% is 7 units, and 65% is 13 units.
Find the gap — The part by which girls are more than boys is 65% − 35%.
Match to pupils — The question says there are 126 more girls than boys. So this extra 30% is 126 pupils.
Find 10% first — 30% is 3 groups of 10%. So 10% = 126 ÷ 3 = 42 pupils.
Find 100% — 100% is 10 groups of 10%, so the total number of pupils is 42 × 10 = 420 pupils. Check: 35% boys is 147, 65% girls is 273, and 273 − 147 = 126. 📌 Key idea: when the difference between two parts is given, find the percentage difference first, then use it to find 100%.

Method: Find the other percentage from 100%, then match the percentage difference to the given number to find 100%.

On a P6 learning journey, 40% of the pupils were boys. There were 72 more girls than boys. How many pupils went on the learning journey altogether?
Answer
360 pupils — Girls = 100% − 40% = 60%. Girls are more than boys by 60% − 40% = 20%. So 20% = 72 pupils. 10% = 36 pupils, so 100% = 360 pupils.
The canteen sold some drinks during recess. 25% of them were iced Milo. The other drinks sold were 180 cups more than the iced Milo. How many cups of drinks were sold altogether?
Answer
360 cups — Other drinks = 100% − 25% = 75%. Difference = 75% − 25% = 50%. So 50% = 180 cups. 100% = 180 × 2 = 360 cups.
At a school concert, 35% of the audience were parents and 20% were teachers. The rest were pupils. There were 90 more pupils than parents. How many people were in the audience altogether?
Answer
900 people — Pupils = 100% − 35% − 20% = 45%. Pupils are more than parents by 45% − 35% = 10%. So 10% = 90 people. 100% = 90 × 10 = 900 people.

An animation walks through each step, then 3 similar questions check it stuck; mistakes come back for review after 1, 3 and 7 days.