SOLVING PROBLEMS ON PERCENTAGE

Problem 1 :

12% of the books in a public library are English books. If there are 92,000 books in the library, find the number of  English books.

Solution :

Number of English books in the library is

= 12% of the total books

= 0.12 ⋅ 92000

= 11,040

Problem 2 :

A boy secured 88% of the total marks in a public examination. The total marks were 1200. How many marks did the boy secure ?

Solution :

Marks scored by the students is

= 88% of the total marks

= 0.88 ⋅ 1200

= 1056

Problem 3 :

A packet contained 450 chocolates. 60% of the chocolates were distributed to the children.

(i) How many chocolates were distributed ?

(ii) How many chocolates remained in the packet ?

Solution (i) :

Number of chocolates were distributed is

= 60% of the packet (450 chocolates)

= 0.60 ⋅ 450

= 270

Solution (ii) :

Number of chocolates remained in the packet after distribution is

= Total no. chocolates - No. of chocolates distributed

= 450 - 270

= 180

Problem 4 :

A man had $360,000 worth of property. He left 60% of his property to his son. How much did his son get ?

Solution :

The worth of property received by the son is

= 60% of the total property

= 0.6 ⋅ 360,000

= $216,000

Problem 5 :

A company gives a bonus of 12½% of the total yearly salary to each of its employees during a year. If an employee gets a monthly salary of $2000, how much bonus will he get ?

Solution :

Monthly salary of the employee = $2000.

Yearly salary of the employee is

= 12 ⋅ 2000

= $24,000

The bonus that the employee will get is

= 12½% of yearly salary

or

= 12.5% of yearly salary

= 0.125 ⋅ 24,000

= $3000

Hence, the employee gets a monthly salary of $2000 will get a bonus of $3000.

Problem 6 :

A person bought a property for $120,000. If he has to pay $2400 to a broker for arranging the purchase, what percent is it of the total purchase value ?

Solution :

Percentage of brokerage of total purchase value is

= (Brokerage amount/Total worth of the property) ⋅ 100 

= (2400/120,000) ⋅ 100 %

= 2%

Problem 7 :

A fruit seller bought 1200 mangoes. 7% of the mangoes were rotten. Find the number of mangoes became rotten.

Solution :

Number of mangoes became rotten is

= 7% of the total mangoes 

= 0.07 ⋅ 1200

= 84

Problem 8 :

In a school, there were 1200 students. 15% of the students went on an excursion. Find the number of students who joined the excursion.

Solution :

Number of students who joined the excursion is

= 15% of the total students

= 0.15 ⋅ 1200

= 180

Problem 9 : 

The population of a town was 320,000. If the population is increased by 4%, find the increase in population.

Solution :

The increases in population is

= 4% of the total population

= 0.04 ⋅ 320,000

= 12,800

Problem 10 :

A person gets a salary of $2800 per month. If he saves 20% of his salary, find his savings per month.

Solution :

The person's savings per month is

= 20% of his monthly salary

= 0.2 ⋅ 2800

= 560

Problem 11 :

If a is 2403% of b + c, and b is 89% of c, what percent of b is a?

Solution :

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