WORD PROBLEMS ON FRACTIONS WITH SOLUTIONS

Problem 1 : 

A fruit merchant bought mangoes in bulk. He sold 5/8 of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy? 

Solution :

Let x be the number of mangoes he bought.

Then,

Number of mangoes sold  =  5x/8

Number of mangoes spoiled  =  x/16

Number of mangoes remaining  =  300

Then, we have

x - (5x/8 + x/16)  =  300

x - (10x/16 + x/16)  =  300

x -11x/16  =  300

16x/16 - 11x/16  =  300

5x/16  =  300

Multiply each side by 16/5.

x  =  300 ⋅ 16/5

x  =  (300 ⋅ 16) / 5

x  =  (60 ⋅ 16) / 1

x  =  960

So, the fruit merchant bought 960 mangoes. 

Problem 2 :

A family requires 2 1/2 liters of milk per day. How much milk would family require in a month of 31 days?  

Solution :

Milk required for a day  =  2 1/2 liters.

Then, the amount of milk (in liters) required for 31 days is

=  31 ⋅ 2 1/2

=  31 ⋅ 5/2

=  (31 ⋅ 5) / 2

=  155/2

=  77 1/2 

So, the family requires 77 1/2 liters of milk for 31 days. 

Problem 3 :

A ream of paper weighs 12 1/2 kg.  What is the weight per quire ?

Solution :

Weight of 1 ream of paper  =  12 1/2 kg

1 ream = 20 quires 

Then, the weight of 1 quire is

=  12 1/2 ÷ 20

=  25/2 ÷ 20

=  25/2 ÷ 20/1

=  25/2 ⋅ 1/20

=  (25 ⋅ 1) / (2 ⋅ 20)

=  (5 ⋅ 1) / (2 ⋅ 4)

=  5/8

So, the weight of 1 quire of paper is 5/8 kg.

Problem 4 :

It was Richard's birthday. He distributed 6 kg of candies to his friends. If he had given 1/8 kg of candies to each friend, how many friends were there ?

Solution :

Total quantity of candies  =  6 kg

Share of each person  =  1/8 kg

Then, number of friends is 

=  6 ÷  1/8

=  6 ⋅ 8/1

=  (6 ⋅ 8) / 1

=  48

So, there were 48 friends. 

Problem 5 :

Rachel bought a pizza and ate 2/5 of it. If he had given 2/3 of the remaining to his friend, what fraction of the original pizza will be remaining now ?

Solution :

Given : Rachel 2/5 of a pizza. 

Remaining  =  3/5

Given : He gave 2/3 of the remaining to his friend.

Then, Amount of pizza given to his friend is 

=  2/3 ⋅ 3/5

=  (2 ⋅ 3) / (3 ⋅ 5)

=  (2 ⋅ 1) / (1 ⋅ 5)

=  2/5

Now, we have

Then, we have 

Remaining pizza  =  1 - (2/5 + 2/5)

Remaining pizza  =  1 - 4/5

Remaining pizza  =  5/5 - 4/5

Remaining pizza  =  1/5

So, 1/5 of the original pizza will be remaining. 

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