WORD PROBLEMS WITH FRACTIONS FOR 5th  GRADE

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? 

(A) 240 mangoes     (B) 160 mangoes     (C) 960 mangoes

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

Total no. of mangoes -(no. of mangoes sold + no. of mangoes spoiled)  =  no. of mangoes remaining

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?  

(A) 77 ½  liters       (B) 65 ½  liters    (C) 61 ½  liters

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 ?

(A) 5/8 kg           (B) 3/8 kg        (C) 1/2 kg

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 ?

(A) 36 Friends         (B) 48  Friends        (C) 96 Friends

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 :

6 students went on a picnic.One student agreed to bear half of the expenses. The remaining 5 students shared the remaining expenses equally. What fraction of the expenses does each of 5 students pay?

(A) x/10      (B) x/ 5   (C) x/2

Solution :

Let x be the expense

Expense beared by one student  =  x/2

Remaining expense  =  x/2

Expense shared by the other 5 students  =  (x/2)/5

=  x/10

Problem 6 :

I have 2 ½ times money that David has. If i have $100, how much money does David have?

(A) $50        (B) $70       (C) $40

Solution :

Let x be the amount that David has, then i will have

(2  1/2) ⋅ x.

That is  5x/2.

5x/2  =  100

5x  =  200

x  =  40

So, the amount that David has is $40.

Problem 7 :

In a basket there are two kinds of sweet packets. There are 7 packets of the first kind each weighing 1 ¼ kg and 9 packets of the second kind each weighing ¾ . What is the total weight of the sweets in the basket?

(A) 15 ½ kg           (B) 12 ½ kg          (C) 10 ½ kg

Solution :

Weight of first kind sweet  =  1  1/4 kg  =  5/4

Weight of second kind sweet  =  3/4 kg

Total weight  =  7 ⋅ (5/4) + 9 ⋅ (3/4)

  =  (35/4) + (27/4)

  =  62/4

  =  31/2

By changing the mixed fraction into improper number, we get 15  1/2 kg.

Problem 8 :

How many half-liter bottles can be filled from a can containing 37 ½ liter of milk? 

(A) 77 bottles      (B) 65 bottles    (C) 75 bottles

Solution :

Quantity of milk  =  37  1/2   =  65/2

Number of half liter bottles can be filled 

  =  (65/2) / (1/2)

  =  (65/2) ⋅ (2/1)

  =  65 bottles

Problem 9 :

A gentleman bought 200 liter of milk for a function. 4/5 of it was used for preparing sweets. 3/4 of the remaining milk was used for preparing coffee. How much of the milk remained ?

(A) 5 liter        (B) 11 liter       (C) 10 liter

Solution :

Original quantity of milk  =  200 liter

Quantity of milk used for preparing sweets 

  =  (4/5) of 200

  =  (4/5) ⋅ 200

=  160

Remaining quantity of milk  =  200 - 160  ==>  40 liter

Quantity of milk used for coffee   =  (3/4) of 40

  =  (3/4) ⋅ 40

=  30 liter

Remaining quantity of milk at the end  =  40 - 30

=  10 liters 

Problem 10 :

Two thirds of a tank can be filled in 18 minutes. How many minutes will it require to fill the whole tank?

(A) 24 minutes      (B) 16 minutes   (C) 27 minutes

Solution :

Let x be the capacity of the tank.

Part of tank filed in 18 minutes  =  2/3 of x

Part of tank to be filled  =  1/3 of x

1/3 of x  =  9 minutes

Time taken to fill the whole tank  =  18 + 9

  =  27 minutes

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