PERCENTAGE INCREASE AND DECREASE

Example 1 :

Increase 20 by 50%

Solution :

Original quantity = 20

Should be increased by 50%.

Original quantity can be considered as 100%.

Then the new quantity = (100 + 50)% of the old quantity

= 150% of 20

= 1.50 (20)

= 30

Example 2 :

Increase 32 by 75%

Solution :

Original quantity = 32

Should be increased by 75%.

Original quantity can be considered as 100%.

Then the new quantity = (100 + 75)% of the old quantity

= 175% of 32

= 1.75 (32)

= 52.5

Example 3 :

Decrease 55 by 40%

Solution :

Original quantity = 55

Should be decreased by 40%.

Original quantity can be considered as 100%.

Then the new quantity = (100 - 40)% of the old quantity

= 60% of 55

= 0.60 (55)

= 33

Example 4 :

Decrease 6 kg by 5%

Solution :

Original quantity = 6

Should be decreased by 5%.

Original quantity can be considered as 100%.

Then the new quantity = (100 - 5)% of the old quantity

= 95% of 6

= 0.95 (6)

= 5.7

Example 5 :

Increase 670 by 1.2%

Solution :

Original quantity = 670

Should be increased by 1.2%.

Original quantity can be considered as 100%.

Then the new quantity = (100 - 1.2)% of the old quantity

= 98.8% of 6

= 0.988 (6)

= 5.928

Example 6 :

When a tennis ball is dropped, it bounces and then rises. The ball rises to 80% of the height from which it is dropped. The ball is dropped from a height of 4 meters.

(a) Calculate the height of the rise after the first bounce.

(b) Calculate the height of the rise after the second bounce.

Solution :

(a) Height of the ball when it is dropped = 4 meters

The ball rises 80% of the original height.

So, 180% of the ball's height = 1.80(4)

= 7.2 meter

Now the height of the ball is 7.2 meter.

(b) Again it will raise 80% of the original height.

So, 180% of 7.2 :

= 1.80 (7.2)

= 12.96

Example 7 :

When a number is first increased by 10% and then reduced by 10%, the number,

a)  does not change    b)  decreases by 1%      c)  increases by 1%

d)  none of these

Solution :

Let x be the required number. After increasing the number 10%, the new number will be

= 110% of x

Reducing 10%, then the new number will be 90% of 110% of x

= 0.90(1.10x)

= 0.99x

= (99/100) of x

So, the original number x decreases by 1%.

Example 8 :

If the side of the square is increased by 25%, then its area is increased by 

a)  25%      b)  55%      c)  40.5%    d)  56.25%

Solution :

Let x be the side length of the square. Since the side length of the square is increased by 25%, the new side length will be 125% of x

Area of square = 125% of x (125% of x)

= 1.25x (1.25x)

= 1.5625x

= (156.25/100) of x

= 156.25% of x

Increased by 56.25%. So, the answer is option d.

Example 9 :

An article listed at 5400 is offered at a discount of 15%. Due to festival season, the shopkeeper allows a further discount of 5%. Find the selling price of the article.

Solution :

Original price of the article = $5400

After announcing 15% discount, the new price = 85% of 5400

= 0.85(5400)

= 4590

Further discount of 5%, then the new price will be 95% of 4590

= 0.95(4590)

= 4360.5

So, the new selling price will be $4361

Example 10 :

A’s income is 25% more than that of B. B’s income is 8% more than that of C. If A’s income is $20250, then find the income of C.

Solution :

Let x be the income of C.

B's income = 108% of C 

A's income = 125% of 108% of C 

= 1.25(1.08C)

Applying A's income, we get

20250 = 1.25(1.08C)

C = 20250/(1.25)(1.08)

C = 15000

So, C's income is $15000.

Example 11 :

A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for $22500. What is the reduced price per kg of tea? Also, find the original price per kg.

Solution :

10% of $22500 = (10/100) × 22500

= $2250

Reduced price of 25 kg tea = $2250

2250/25

= $90 per kg

Reduced price per kg = $25

Since, the reduction was 10% so the original price = $100 per kg.

Example 12 :

60 is reduced to 45. What percent is the reduction?

Solution :

Percentage change = (old value - new value)/old value x 100%

= [(60 - 45)/60] x 100%

= (15/60) x 100%

= 25%

Example 13 :

If 80 is increased to 125, what is the increase percent?

Solution :

Percentage change = (old value - new value)/old value x 100%

= [(125 - 80)/80] x 100%

= (45/80) x 100%

= 56.25%