PERCENTAGE INCREASE AND DECREASE

Example 1 :

Increase $5000 by 20%.

Solution :

= (100 + 20)% of 5000

= 120% of 5000

= (120/100) x 5000

= 1.20 x 5000

= 6000

When $5000 is increased by 20%, it is $6000.

Example 2 :

Decrease $85 by 22%.

Solution :

= (100 - 22)% of 85

= 78% of 85

= (78/100) x 85

= 0.78 x 85

= 66.3

When $85 is increased by 22%, it is $66.30.

Example 3 :

Increase 78 kg. by 3%.

Solution :

= (100 + 3)% of 78

= 103% of 78

= (103/100) x 78

= 1.03 x 78

= 80.34

When 78kg. is increased by 3%, it is 80.34 kg.

Example 4 :

Increase 800 m by 15%

Solution :

= (100 + 15)% of 800

= 115% of 800

= (115/100) x 800

= 1.15 x 800

= 920

When 800 m. is increased by 15%, it is 920 m.

Example 5 :

What is the overall effect of increasing $100 by 10% and then decreasing the result by 10%? 

Solution :

Increase $100 by 10%.

=  (100 + 10)% of 100

= 110% of 100

= (110/100) x 100

= 110

When $100 is increased by 10%, it is $110.

Decrease $110 by 10%.

=  (110 - 10)% of 110

= 90% of 110

= (90/100) x 110

= 0.9 x 110

= 99

When $110 is decreased by 10%, it is $99.

After the two changes (10% increase and 10% decrease), the original amount $100 becomes $99.

The original quantity 100 is decreased by 1.

Therefore, the overall effect is 1% decrease.

Example 6 :

When decreasing a quantity by 10% in two successive years, the overall result is to decrease the original by 19%, verify.

Solution :

Let the original quantity be 100.

Decrease 100 by 10%.

=  (100 - 10)% of 100

= 90% of 100

= (90/100) x 100

= 0.9 x 100

= 90

Decrease 90 by 10%.

=  (100 - 10)% of 90

= 90% of 90

= (90/100) x 90

= 0.9 x 90

= 81

When decreasing by 10% in two successive years, the original quantity 100 becomes 81.

Decrease 100 by 19% :

=  (100 - 19)% of 100

= 81% of 100

= (81/100) x 100

= 0.81 x 100

= 81

In both ways, we get the same answer.

Decreasing a quantity by 10% in two successive years and decreasing the original quantity by 19% are equal.

Example 7 :

Find the overall effect of increasing a quantity by 20% each year for 3 successive years.

Solution :

Let 100 be the original quantity.

Increase 100 by 20% :

= (100 + 20)% of 100

= 120% of 100

= (120/100) x 100

= 1.20 x 100

= 120

Increase 120 by 20% :

= (100 + 20)% of 120

= 120% of 120

= (120/100) x 120

= 1.20 x 120

= 144

Increase 144 by 20% :

= (100 + 20)% of 144

= 120% of 144

= (120/100) x 144

= 1.20 x 144

= 172.8

After increasing a quantity by 20% each year for 3 successive years, the original quantity 100 becomes 172.8

The original quantity 100 is increased by 72.8.

Therefore, the overall effect is 72.8% increase.

Example 8 :

Increase 150 by 10% and decrease the same by 15%. Find the new number in each case.

Solution :

Increase 150 by 10% :

= (100 + 10)% of 150

= 110% of 150

= (110/100) x 150

= 1.1 x 150

= 165

Decrease 150 by 10% :

= (100 - 10)% of 150

= 90% of 150

= (90/100) x 150

= 0.9 x 150

= 135

Example 9 :

A product has been priced $80. If the product is sold on 20% discount, how much has to be paid for the product?

Solution :

Price of the product after 20% discount :

= (100 - 20)% of 80

= 80% of 80

= (80/100) x 80

= 0.8 x 80

= 64

$64 has to be paid for the product.

Example 10 :

The price of a garment is $90 and now it is on a sale of 10% off. If there is a sales tax of 5%, How much has to be paid for the garment?

Solution :

Price of the product after 10% off :

= (100 - 10)% of $90

= 90% of $90

= (90/100) x 90

= 0.9 x 90

= $81

Increase 81 by 5% (sales tax).

= (100 + 5)% of 81

= 105% of 81

= 1.05 x 81

= 85.05

$85.05 has to paid for the garment.

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