WORD PROBLEMS ON FINDING PERCENT OF QUANTITY

Problem 1 :

Li scored 75% in her test out of 32. What mark did she score ?

Solution :

Total score = 32

Percentage of marks scored by Li = 75%

= 75% of 32

= 0.75(32)

= 24

So, he has score 24 marks out of 32.

Problem 2 :

John scored 70% for an examination marked out of 120. How many marks did he actually get ?

Solution :

Total marks = 120

Percentage of marks scored by John = 70%

John has scored = 70% of 120

= 0.70 (120)

= 84

So, John has scored 84 marks.

Problem 3 :

A Petroleum company claims that cars using new premium unleaded fuel will travel 112% of the distance travelled on regular unleaded. If Geoff can travel 584 miles on a tank of regular fuel, how far should he be able to travel on premium unleaded ?

Solution :

Geoff can cover the distance of 584 miles using regular fuel.

Distance he can cover using unleaded fuel = 112% of 584

= 1.12(584)

= 654.08 miles

So, he can cover 654 miles using premium unleaded fuel.

Problem 4 :

Paula receives 7 1/2% of the net profits on a book she helped to write. If the net profits this year is $38700, how much will she receive in royalties.

Solution :

Net profit = 38700

= 7 1/2 % of 38700

= 15/2% of 38700

= 7.5% of 38700

= 0.075 (38700)

= 2902.5

So, she will get $2902.

Problem 5 :

Nicki is part of syndicate that owns researchers. He owns 28% of Peter Pan, who last week won $18600 in the derby. How much should Nicki receive ?

Solution :

Percentage of money won by Peter Pan = 18600

Amount Nicki has = 28% of 18600

= 0.28 (18600)

= 5208

Problem 6 :

A restaurant charges 7  1/2% service on the total bill. If Jack and Jill buy food and wine to the value of $54, how much will they have to pay

(a) a service

(b) in total ?

Solution :

(a) Value of food that Jack and Jill buy = $54

Service charge = 7  1/2% of 54

= 15/2% of 54

= 0.075 (54)

= 4.05

(b) In total they have to pay = 54 + 4.05

= 58.05

Problem 7 :

A signed west tigers jumper purchased for $800 and was sold for $2000.

a) Calculate the profit

b) Express a profit as a percentage of the cost price.

Solution :

a) 

Cost price = $800

Selling price = $2000

Profit = 2000 - 800

= 1200

Profit percentage = (1200 / 2000) x 100%

= 0.6 x 100%

= 60%

b) 

Percentage of profit in cost price = (1200/800) x 100%

= 1.5 x 100%

= 150%

Problem 8 :

Daniel earns $720 per week. He spends 45% of his income on rent and house hold expenditure, 22% on entertainment and the remainder is placed in a saving account. Calculate the amoutn of money Daniel allocates each week to 

a)  rent and household expenditure

b) entertainment

c) savings

Solution :

His earning = $720

a) Percentage of amount spent for rent and house hold expenditure

= 45% of 720

= 0.45 (720)

= $324

b) Percentage of amount spent for entertainment = 22% of the remainder.

= 22% of (720 - 324)

= 0.22 (396)

= $87.12

c) Percentage of amount for savings = 100 - (45 + 22) 

= 100 - 67

= 33% of (720 - 324 - 87.12)

= 0.33 (750 - 411.12)

= 0.33(338.88)

= $111.8

Problem 9 :

Decrease 280 by 25%

Solution :

Original quantity can be considered as 100%

Decreasing 25%, we get

= 75% of 280

= 0.75(280)

= 210

So, after decreasing it by 25% we get $210.

Problem 10 :

The amount of water in a water tank increases from 80 L to 135L. What is the percentage increase ?

Solution :

Original quantity = 80 L

Increases to = 135 L

Amount increase = 135 - 80

= 55

= (55/80) x 100%

= 0.6875 x 100%

= 68.75%

Problem 10 :

£50 is worth €56

(a) How many euros is £1 worth?

(b) How many euros is £220 worth?

Solution :

£50 is worth €56

a)

£1 = €56/50

£1 = €1.12

b) 

£220 = €1.12 x 220

= €246.4

Problem 11 :

An antique gun purchased for $1200 was later sold for $2900

(a) Calculate the profit.

(b) Express the profit as a percentage of the cost price.

Solution :

Cost price = $1200

 Selling price = $2900

a) Profit = Selling price - cost price

= 2900 - 1200

= 1700

Profit = (1700/2900) x 100%

= 0.586 x 100%

= 58.6%

b)  

Profit % = (1700/1200) x 100%

= 1.41 x 100%

= 141%