RATIO AND PROPORTION PROBLEMS

Problem 1 :

If there are two lengths such that a = 90 cm and b = 120 cm, then find the ratio between them.

Solution :

a : b = 90 : 120

a : b = 3 : 4

So, the ratio between the two lengths is

3 to 4

Problems 2-8 refer to the following information.

Problem 2 :

Find the ratio of the age of John to David.

Solution :

Age of John  =  17 years

Age of David  =  15 years

Age of John : Age of David  =  17 : 15

So, the ratio of the age of John to David is

17 to 15

Problem 3 :

Find the ratio of the age of David to John.

Solution :

Age of David = 15 years

Age of John = 17 years

Age of David : Age of John = 15 : 17

So, the ratio of the age of David to John is

15 to 17

Problem 4 :

Find the ratio of the weight of David to John.

Solution :

Weight of David = 29 kg

Weight of John = 31 kg

Weight of David : Weight of John = 29 : 31

So, the ratio of the Weight of David to John is

29 to 31

Problem 5 :

Find the ratio of the height of John to David.

Solution :

Height  of John is

= 1m + 36cm

= 100cm + 36cm

= 136 cm

Height of David = 123 cm

Height of John : Height of David = 136 : 123

So, the ratio of the height of John to height of David is

136 to 123

Problem 6 :

Find the ratio of studying time of John to David.

Solution :

Studying time of John  is

= 4 hours

= 4 ⋅ 60 min

= 240 minutes

Studying time of David = 180 minutes.

Studying time --> John : David = 240 : 180

Studying time --> John : David = 4 : 3

So, the ratio of studying time of John to David is

4 to 3

Problem 7 :

Find the ratio of speed of cycling between John and David.

Solution :

Speed of cycling  of John = 10 kmph.

Speed of cycling of David = 15 kmph.

Speed of cycling --> John : David = 10 : 15

Speed of cycling --> John : David = 2 : 3

So, the ratio of speed of cycling between John and David is

2 to 3

Problem 8 :

Find the ratio of playing time of John to David.

Solution :

Playing time of John = 2 hours

Playing time of David = 1 hour

Playing time --> John : David = 2 : 1

So, the ratio of playing time of John to David is

2 to 1

Problem 9 :

A student has 12 note books and 8 text books. Find the ratio of the note books to text books.

Solution :

No. of note books = 12

No. of textbooks = 8

No. of note books : No. of textbooks = 12 : 8

No. of note books : No. of textbooks = 3 : 2

So, the ratio of notebooks to textbooks is

3 to 2

Problem 10 :

The cost of a pen is $3 and the cost of pencil is $1.50. Find the ratio of the cost of a pen to pencil.

Solution :

Cost of a pen = $3 = 3 ⋅ 100 = 300 pennies

Cost of a pencil = $1.50 = 1.50 ⋅ 100 = 150 pennies

Cost of a pen : Cost of a pencil = 300 : 150

Cost of a pen : Cost of a pencil = 2 : 1

So, the ratio of cost of a pen to pencil is

2 to 1

Problems 11-13 refer to the following information.

In a Village of 10,000 people, 4,000 are Government Employees and the remaining are self-employed.

Problem 11 :

Find the ratio of the government employees to people of the village. 

Solution :

No. of government employees = 4000

Total no. of people in the village = 10000

Government employees : Village people = 4000 : 10000

= 2 : 5

Hence, the ratio of government employees to village people is

2 to 5 

Problem 12 :

Find the ratio of self employed to people of the village. 

Solution :

No. of self employed is

= 10000 - 4000

= 6000

Total no. of people in the village = 10000

Self employed : Village people = 6000 : 10000

= 3 : 5

Hence, the ratio of self employed to village people is

3 to 5 

Problem 13 :

Find the ratio of self employed to government employees. 

Solution :

No. of self employed is

= 10000 - 4000

= 6000

No. of government employees = 4000

Self employed : Government employees = 6000 : 4000

Self employed : Government employees = 3 : 2

Hence, the ratio of self employed to government employees is

3 to 2 

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