Percentages greater than 100

The idea

A quantity larger than the reference value is more than 100% of it: p% means p/100 times the reference, so a percentage above 100 shows the quantity is (p – 100)% more than the reference.

Can a percentage be more than 100?

Kishanlal aims for daily sales of at least ₹5,000. On Day 3 he sold exactly ₹5,000. On Day 4 he sold ₹6,000, which is ₹1,000 more than his target.

What percentage of his target did he reach on Day 4?

• 60%
• 100%
• 120%

Slide the sales past the target

The bar goes from ₹0 to ₹12,500. The black mark is the target, which is 100%. Slide the sales and watch the percentage, especially after the mark.

Beyond 100%

A quantity larger than the reference value is more than 100% of it: p% means p/100 times the reference, so a percentage above 100 shows the quantity is (p − 100)% more than the reference.

Day 3: ₹5,000 is exactly the target, so it is 100%. Day 4: ₹6,000 is ₹1,000 more than the target. 1000 is 20% of 5000, so 6000 is 100% + 20% = 120% of the target, which is 20% more.

Check: 6000/5000 × 100 = 120 So 120% of the target means 1.2 times the target.

Other days: ₹2,500 is 1/2 the target, or 50%, or 0.5 of it. ₹10,000 is twice the target, or 200%.

Notes

A quantity larger than the reference value is more than 100% of it: p% means p/100 times the reference, so a percentage above 100 shows the quantity is (p − 100)% more than the reference.

Check yourself

A farmer harvested 260 kg of wheat last year and 650 kg this year. This year's harvest is what percentage of last year's?

Answer: 250 %

650/260 × 100 = 250%. This year's harvest is 250% of last year's, which is 2.5 times.

A school had 400 students last year and has 500 this year. This year's number is what percentage of last year's?

Answer: 125 %

500/400 × 100 = 125%. That is 100% + 25%: the school grew by 25%.

A shop's sales target is ₹8,000. Today's sales were 150% of the target. How much were the sales? (in ₹)

Answer: 12000

150% of 8000 = 150/100 × 8000 = 12,000. The sales were ₹12,000, which is ₹4,000 more than the target.

The population of a town is 175% of what it was 20 years ago. Which statement says the same thing?

• The population has increased by 75% — correct. Yes! 175% = 100% + 75%, so it is 75% more than before.
• The population has increased by 175%. That would be 100% + 175% = 275% of the old population. 175% of it is 75% more.
• The population has decreased by 25%. It is more than 100%, so the population grew. It did not decrease.
• The population has increased by 25%. That would be 125% of the old population. 175% is 75% more.