**Worksheet on Ratio and Proportion :**

Worksheet given in this section is much useful to the students who would like to practice problems on ratio and proportion.

**Problem 1 :**

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

From problem 2 to problem 8, please use the information in the table given below.

**Problem 2 :**

Find the ratio of the age of John to David.

**Problem 3 : **

Find the ratio of the age of David to John.

**Problem 4 :**

Find the ratio of the weight of David to John.

**Problem 5 :**

Find the ratio of the height of John to David.

**Problem 6 :**

Find the ratio of studying time of John to David.

**Problem 7 :**

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

**Problem 8 :**

Find the ratio of playing time of John to David.

**Problem 9 :**

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

**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.

**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

Hence, the ratio between the two lengths is

3 to 4

From question no. 2 to question no.8, please use the information in the table given below.

**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

Hence, 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

Hence, 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

Hence, 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

Hence, 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

Hence, 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

Hence, 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

Hence, 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

Hence, 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

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

2 to 1

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