EXPRESS ONE QUANTITY AS A PERCENTAGE OF ANOTHER

Example 2 :

Mohammed scored 66 marks out of 70 for his chemistry test. What was his percentage ?

Solution :

Marks scored by Mohammed = 66

Total marks = 70

Writing it as fraction, we get

= 66/70

Converting it into percentage = (66/70) x 100%

= 94.28

Approximately 94.3%.

Example 3 :

Erika was late for her bus 3 days out of 22 last month. What percentage of days was she on time ?

Solution :

Number of days she comes late = 3

Total number of day = 22

Writing it as fraction, we get

= 3/22

Converting it as percentage = (3/22) x 100%

= 13.6%

Percentage of days she was on time = 100 - 13.6

= 86.4%

Example 4 :

Phyills sells new cars. Her sales quota for last month was 35 cars. If she sold 43 cars during the month, write this as a percentage of the quota ?

Solution :

Number of cars sold last month = 35 cars

Number of cars sold for this month = 43 cars

Writing it as fraction, we get

= (35/43)

Converting it as percentage, we get

= (35/43) x 100%

= 0.813 x 100%

= 81.3%

Example 5 :

Pierre had $5 in his pocket until he spent 85 cents on some sweets. What percentage of his money did Pierre spend ?

Solution :

Money he has = $5

Money he spent = 0.85

Percentage of money he has spent = (0.85/5) x 100%

= 0.17 x 100%

= 17%

So, 17% of money he has spent.

Example 6 :

Sven walks 475 meters to the underground station, then makes a 3.5 km journey by a train. What percentage of the total distance travelled was on foot ?

Solution :

Distance covered by train = 3.5 km

= 3.5 x 1000

= 3500 meter

Distance covered by walk = 475

Required percentage = (475/3500) x 100%

= 13%

Example 7 :

Leah ate 250 grams of cake from a cake weighing 1  1/2 kg. What percentage of the cake did she eat ?

Solution :

Quantity of cake = 250 grams

Weight of cake = 1 1/2 kg

Converting into grams, we get = 1500 grams

Percentage of cake she eat = (250/1500) x 100%

= 16.6%

= 17%

Example 8 :

Express 4.5 m as a percentage of 120 cm.

Solution :

Original quantity = 120 cm

Converting 4.5 m as cm.

1 m = 100 cm

4.5 m = 450 cm

= (450/120) x 100%

= 3.75 x 100%

= 375%

Example 9 :

Express 660 g as a percentage of 1.2 kg

Solution :

Original quantity = 1.2 kg

1 kg = 1000 grams

1.2 kg = 1.2 x 1000

= 1200 grams

= (660/1200) x 100%

= 0.55 x 100%

= 55%

Example 10 :

Over a period of time the value of a house increased by 15% to $564000. Find the original value of the house, to the nearest dollar.

Solution :

Let x be the original price.

Increased by 15%

115% of x = 564000

1.15x = 564000

x = 564000/1.15

x = 490434.78

Original price is $490434.

Example 11 :

Find 100% of a quantity if 38% is $29.64 kg.

Solution :

Let x be the original quantity.

38% of x = 29.64

0.38 x = 29.64

x = 29.64/0.38

x = 78

100% of the original quantity is $78.

Example 12 :

The brouchure advertises jackets for 30% off the original price. Calculate the original cost if the sale price is $455.

Solution :

Let x be the original quantity.

offer = 30%

Then 70% of x = 455

0.70x = 455

x = 455/0.70

x = 650

So, the orignal price is $650.

Example 13 :

The price of a concert tickets is increased by 74% to $374.10. Calculate the original price.

Solution :

Let x be the original quantity.

174% of x = 374.10

1.74 x = 374.10

x = 374.10/1.74

= 215

So, the original price is $215.

Example 14 :

The radio controlled plane with a cost price $349 is sold at a loss of 23%. Calculate the selling price.

Solution :

Cost price = $349

loss = 23%

Selling price = (100 - 23)% of 349

= 77% of 349

= 0.77(349)

= $268.73

Selling price is $268.73

Example 15 :

The collector card was sold for $475. This was profit of 35%. Calculate the cost price.

Solution :

Selling price = $475

Profit = 35%

It includes 35% increase.

Let x be the cost price

135% of x = 475

1.35x = 475

x = 475/1.35

= 351.8

So, the cost price is $351.8