WORD PROBLEMS ON RATIO

Problem 1 :

Bob has 12 red cards and 20 green cards. What is the ratio of Bob's red cards to this green cards ?

Solution :

Number of red cards = 12

Number of green cards = 20

Red cards : Green cards = 12 : 20

HCF(12, 20) is 4

Dividing each part by 2.

= 3 : 5

Problem 2 :

In a party 10 soft drinks are required for every 12 guests. If there are 252 guests, how many soft drinks is required.

Solution :

Number of soft drinks = 10

Number of guests = 12

Soft drink : Guest = 10 : 12

Let x be the number of soft drinks required.

10 : 12 = x : 252

Writing each ratio as fraction, we get

10/12 = x/252

Multiplying by 252 on both sides, we get

(10/12) ⋅ 252 = x

10 ⋅ 21 = x

x = 210

Problem 3 :

In Jack's class, 18 of the students are tall and 10 are short. In Michael's class 54 students are tall and 30 students are short. Which class has a higher ratio of tall to short students ?

Solution :

Ratio between tall to short students in Jack's class

= 18 : 10

HCF(18, 10) is 2.

Dividing both parts by 2, we get

= 9 : 5

Ratio between tall to short students in Michael's class

= 54 : 30

HCF(54, 30) is 6.

Dividing both parts by 6, we get

= 9 : 5

So, ratio between tall to short is the same in both classes.

Problem 4 :

The price of 3 apples at the Quick Market is $1.44. The price of 5 of the same apples at Walmart is $2.50. Which place is the better buy ?

Solution :

At Quick Market :

Price of 3 apples = $1.44

Cost of 1 apple = 1.44/3 ==> 0.48

Price at Walmart :

Price of 5 apples = $2.50

Cost of 1 apple = 2.50/5 ==> 0.5

0.48 < 0.5

So, Quick market is the best place.

Problem 5 :

The bakers at the Bakery can make 160 bagels in 4 hours. How many bagels can they bake in 16 hours? What is the rate per hour ?

Solution :

Let "x" be the number of bagels he can make in 16 hour.

Writing the given information as ratio, we get

Number of bagels : number of hours  =  160 : 4

160 : 4 = x : 16

160/4 = x/6

Multiplying by 6 on both sides.

40(6) = x

x = 240

So, the baker can make 240 bagels in 16 hours.

Problem 6 :

The ratio of the boys to girls in a class is 2 : 3. If there are 18 boys in the class, how many girls  are in that class ?

Solution :

Ratio between boys to girls = 2 : 3

Number of boys = 2x and number of girls = 3x

Given number of boys = 18

2x = 18

x = 18/2

x = 9

Number of girls = 3(9)

= 27

So, there are 27 class in the class.

Problem 7 :

The ratio of red marbles to blue marbles in the bag is 3 : 4. If there are 42 marbles in the bag, how many of the marbles are red ?

Solution :

Ratio between red to blue marble is 3 : 4

Let number of red marble = 3x

Blue marble = 4x

Total number of marbles = 3x + 4x ==>  7x

7x = 42

Dividing by 7 on both sides, we get

x = 42/7

x = 6