WORD PROBLEMS ON FRACTION OF QUANTITIES

Problem 1 :

2/3 of the birds in my aviary are finches. If there are 24 birds in my aviary, how many finches are there?

Solution :

Total number or birds = 24

Number of birds that are finches = 2/3 of total number of birds

= 2/3 × 24

= 16 finches

So, 16 finches are there in aviary.

Problem 2 :

One morning two fifths of the passengers on my bus were school children. If there were 45 passengers, how many were school children?

Solution :

Total number of Passengers = 45

Total number of children in the bus

= 2/5 of total number of passenger

= 2/5 × 45

= 18 children

So, there are 18 school children on the bus.

Problem 3 :

Richard spent three quarters of his working day installing computers, and the remainder of the time travelling between jobs. If his working day was 8 hours, how much time did he spend travelling?

Solution :

Time taking for installing computers = 3/4 of time spent

Time spent for travelling between jobs = 1/4 of time spent

Working hours = 8 hours

= 1/4 × 8

= 2 hours

Time spent for travelling is 2 hours.

Problem 4 :

When Sasha played netball, she scored a goal with seven eighths of her shots for goal. If she shot for goal 16 times in a match, how many goals did she score?

Solution :

She scores = 7/8 of number of shoots

Number of shoots  = 16 times

= (7/8) × 16

= 14 goals

So, she scored 14 goals in a match.

Problem 5 :

A business hired a truck to transport boxes of equipment. The total weight of the equipment was 3000 kg, but the truck could only carry 5/8 of the boxes in one load.

a.   What weight did the truck carry in the first load?

b.   If there were 80 boxes, how many did the truck carry in the first load?

Solution :

a.

Weight of equipment = 3000 kg

Weight truck can carry 5/8 of the total weight = 5/8 × 3000

= 1875 kg

b.

= 5/8 × 80

= 50 boxes

So, 50 boxes truck carry in the first load.

Problem 6 :

In an aquarium, 2/5 of the fish are surgeon fish. Of these, 3/4 are yellow tangs. What fraction of all fish in the aquarium are yellow tangs?

Solution :

Quantity if surgeon fish = 2/5

Quantity of yellow tangs = 3/4 of 2/5

= 3/4 x 2/5

= 3/10

So, 3/10 are yellow tangs.

Problem 7 :

Sameer has 465 toffees that he wants to distribute on his birthday. He distributes 1/5 of these in the class. Out of the remaining toffees, he contributes 2/3 of his teachers. What is the number of toffees remaining with him ?

Solution :

Total number of toffees Sameer has = 465

Number of toffees he distributes in the class = 1/5 of 465

= (1/5) x 465

= 465/5

= 93

Number of remaining toffees after distributing to the class = 465 - 93

= 372

Number of toffees he distributes to his teacher = 2/3 of 372

= (2/3) x 372

= 248

Number of toffees remaining = 465 - (93 + 248)

= 465 - 341

= 124

Problem 8 :

Mr. Ben got a job at the age of 23 years and he got retired from the job a the age of 60 years. What fraction of his till retirement was he in the job ?

Solution :

Number of years he is in job = 60 - 23

= 37

Fraction part he is in the job = 37/60

Problem 9 :

There are 12 dozen egg crates. 7/24 of them are rotten and 1/3 of them are to be sent back. How many crates can be used ?

Solution :

Number of egg crates = 12 dozen

1 dozen = 12

= 24(12)

= 288

Number of rotten = 7/24 of 288

= (7/24) x 288

= (7 x 288)/24

= 84

Number of eggs sent back = 1/3 of 288

= 96

Number of eggs used = 288 - (84 + 96)

= 288 - 180

= 108

Problem 10 :

Kabir exercised for 3/6 of an hour, while Rohit exercised 3/4 of an hour. Who exercised longer time ?

Solution :

Total number of hours in a day = 24

Number of hours exercised by Kabir = 3/6 of 24

= (3/6) x 24

= 3 x 4

= 12 hours

Number of hours exercised by Rohit = 3/4 of 24

= (3/4) x 24

= 3 x 6

= 18 hours

So, Rohit took longer time for exercise.

Problem 11 :

A rectangle is divided in to certain number of equal parts. If 20 of the parts so formed represent the fraction 1/5, find the number of parts in which rectangle has been divided ?

Solution :

Let x be the certain number of parts.

1/5 of certain number of parts = 20

1/5 of x = 20

(1/5) ⋅ x = 20

x = 20(5)

x = 100

So, the required number of certain parts is 100.