Percentage

Percentage

A fraction which has 100 as its denominator is known as a Percentage.

Decimal to Percentage

Multiply decimal by 100%

0.27 = 0.27 × 100% = 27%

1.27 = 1.27 × 100% = 127%

0.027 = 0.027 × 100% = 2.7%

Percentage to Decimal

Divide percentage by 100

27% = 27/100 = 0.27

127% = 127/100 = 1.27

2.7% = 2.7/100 = 0.027

Percentage Change

Percentage Change = (change/original) x 100%

The price of an item is increased from $90 to $108. Find the percentage increase in price.

Change in price = 108 – 90 = 18

Percentage Change = (18/90) x 100% = 20%

Comparing Quantities

To convert one quantity as a percentage of another quantity both must be in same units.

A = 100g

B = 1kg = 1000g

A as percentage of B = (100/1000) x 100% = 10%

B as percentage of A = (1000/100) x 100% = 1000%

Percentage Increase or Decrease

Take the given quantity as 100%, to increase or decrease it by a given percentage.

Increase 250 g by 10%

100% = 250 g

110% = (250/100) x 110 = 275 g

Decrease 250 g by 10%

100% = 250 g

90% = (250/100) x 90 = 225 g

Increase 3 km by 20%

100% = 3 km

120% = (3/100) x 120 = 3.6 km

Decrease 3 km by 20%

100% = 3 km

80% = (3/100) x 80 = 2.4 km

ExampleS

The price of an item in January was $120. The price is increased by 30% from January to February and it is decreased by 20% from February to March.

(a) Find the price of the item in February

(b) Find the price of the item in March

(c) Percentage increase in price from January to March

(a) Price of the item in February = (130/100) x $120 = $156

(b) Price of the item in March = (80/100) x $156 = $124.80

Increase in price from January to March = 124.80 - 120 = 4.80

(c) Percentage increase from January to March = (increase in price /original price) x 100%

= (4.80/120) x 100% = 4%

40% of balloon in a bag is of red colour, 28% are blue colour and the rest are yellow colour. If there are 96 yellow colour balloons in the bag.

(a) Find the total number of balloons in the bag

(b) Find the number of blue colour balloons

(c) If 100 more red colour balloons are added to the bag, find the percentage of Yellow colour balloons now

(a) Percentage of Yellow colour ballons = 100% - 40% - 28% = 32%

Number of yellow colour balloons = 96

32% --> 96

Total number of balloons in the bag = 100% --> (96/32) x 100 = 300

(b) Number of Blue colour balloons in the bag = (28/100) x 300 = 84

(c) When 100 more red colour balloons are added to the bag, total number of balloons become 300 + 100 = 400

Percentage of Yellow Colour Balloons = (96/400) x 100% = 24%

Questions

1. Ahmed reads 200 pages of a book on Monday, 40% of the remainder on Tuesday and the balance 240 pages on Wednesday. Find the total number of pages in the book.
2. A pen is sold for $2 in 2018 which is 25% more than the price in 2017. Find the selling price of the pen in 2017.
3. During a Sale, all items in the shop were sold at a discount of 20%. Find the original price of a TV, that is sold for $960 during the Sale.
4. A Car Salesman, Jimmy earns a fixed Salary of $2000 and 1% Commission on all his Car Sales. In a month, he sold five cars at $80,000 each. Find his total income for that month.
5. A Fish gains 10% in weight every month. At the beginning of January it weighs 1200 g. Find its weight at the beginning of March.
6. House price appreciates 5% every year. In January 2010, price of a house is 200,000. Find its price in January 2013.
7. A farmer has 200 Chickens in his farm. He also has 60% less Cows than Chicken and 20% more Sheeps than Cows. Find the total number of animals in his farm.
8. Length of each side of a Square is increased by 10%. Find the percentage increase in its Area.