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## NCERT Solutions for Class 6 Maths Chapter 12: Ratio and Proportion Ex 12.1

**Question 1:**

**There are 20 girls and 15 boys in a class.**

**(a) What is the ratio of number of girls to the number of boys?**

**(b) What is the ratio of girls to the total number of students in the class?**

**Solution**:

Total number of students in the class is,

20 + 15 = 35

(a) The ratio of girls to boys is 20/15=4/3=4:3

(b) The ratio of girls to all the students in class is 20/35=4/7=4:7

**Question 2:**

**Out of 30 students in a class, 6 like football, 12 like cricket and remaining**

**like tennis. Find the ratio of:**

**(a) Number of students liking football to number of students liking tennis.**

**(b) Number of students liking cricket to total number of students.**

**Solution**:

Out of 30 students, if 6 like football and 12 like cricket, then 12 students like tennis.

(a) Students liking football to the number of students liking tennis is, 6/12=1/2=1:2

(b) Students liking cricket to all the students is 12/30=2/5=2:5

**Question 3:**

**See the figure and find the ratio of:**

**(a) Number of triangles to the number of circles inside the rectangle.**

**(b) Number of squares to all the figures inside the rectangle.**

**(c) Number of circles to all the figures inside the rectangle.**

**Solution**:

(a) Number of triangles to number of circles is, 3/2=3:2

(b) Number of squares to all the figures inside the rectangle, 2/7=2:7

(c) Number of circles to all the figures inside the rectangle, 2/7=2:7

**Question 4:**

**Distances travelled by Hamid and Akhtar in an hour are 9 km and 12 km.**

**Find the ratio of speed of Hamid to the speed of Akhtar.**

**Solution**:

We know that speed = distance/time so,

Speed of Hamid = 9/1= 9 km/hr.

Speed of Akhtar =12/1= 12 km/hr.

The ratio of speed of Hamid to Akhtar is, 9/12=3/4==3:4

**Question 5:**

**Fill in the following blanks:**

**[Are these equivalent ratios?]**

**Solution**:

**Question 6:**

**Find the ratio of the following:**

**(a) 81 to 108 (b) 98 to 63**

**(c) 33 km to 121 km (d) 30 minutes to 45 minutes**

**Question 7:**

**Find the ratio of the following:**

**(a) 30 minutes to 1.5 hours (b) 40 cm to 1.5 m**

**(c) 55 paise to Re. 1 (d) 500 ml to 2 litres**

**Question 8:**

**In a year, Seema earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of:**

**(a) Money that Seema earns to the money she saves.**

**(b) Money that she saves to the money she spends.**

**Question 9:**

**There are 102 teachers in a school of 3300 students. Find the ratio of the**

**number of teachers to the number of students.**

**Question 10:**

**In a college out of 4320 students, 2300 are girls. Find the ratio of:**

**(a) Number of girls to the total number of students.**

**(b) Number of boys to the number of girls.**

**(c) Number of boys to the total number of students.**

**Question 11:**

**Out of 1800 students in a school, 750 opted basketball, 800 opted cricket**

**and remaining opted table tennis. If a student can opt only one game, find**

**the ratio of:**

**(a) Number of students who opted basketball to the number of students**

**who opted table tennis.**

**(b) Number of students who opted cricket to the number of students opting**

**basketball.**

**(c) Number of students who opted basketball to the total number of**

**students.**

**Question 12:**

**Cost of a dozen pens is ₹ 180 and cost of 8 ball pens is ₹ 56. Find the ratio of ****the cost of a pen to the cost of a ball pen.**

**Question 13:**

**Consider the statement:**

**Ratio of breadth and length of a ball is 2 : 5. Complete the following that**

**shows some possible breadths and lengths of the hall**

**Question 14:**

**Divide 20 pens between Sheela and Sangeeta in the ratio 3: 2.**

**Question 15:**

**Mother wants to divide ₹ 36 between her daughters Shreya and Bhoomika**

**in the ratio of their ages. If the age of Shreya is 15 years and age of**

**Bhoomika is 12 years, find how much Shreya and Bhoomika will get.**

**Question 16:**

**Present age of father is 42 years and that of his son is 14 years. Find the**

**ratio of:**

**(a) Present age of father to the present age of son.**

**(b) Age of the father to the age of the son, when son was 12 years old.**

**(c) Age of father after 10 years to the age of son after 10 years.**

**(d) Age of father to the age of son when father was 30 years old.**

## NCERT Solutions for Class 6 Maths Chapter 12: Ratio and Proportion Ex 12.2

**Question 1:**

**Determine the following are in proportion:**

**(a) 15, 45, 40, 120**

**(b) 33, 121, 9, 96**

**(c) 24, 28, 36, 48**

**(d) 32, 48, 70, 210**

**(e) 4, 6, 8, 12**

**(f) 33, 44, 75, 100**

**Solution**:

Therefore 33, 44, 75, 100 are in proportion