Introduction
Introduction - Ratio and Proportion - Chapter 12 - Class 6th Maths
Q 1 - Ex 12.1 - Ratio and Proportion - NCERT Maths Class 6th - Chapter 12
Page No 251:
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 number of girls to the total number of students in the class?
Answer:
Number of girls = 20Number of boys = 15
Total number of students = 20 + 15 = 35
(a) Ratio of number of girls to boys =
(b) Ratio of number of girls to total students =
Q 2 - Ex 12.1 - Ratio and Proportion - NCERT Maths Class 6th - Chapter 12
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.
Answer:
Number of students who like football = 6Number of students who like cricket = 12
Number of students who like tennis = 30 − 6 − 12 = 12
(a) Ratio of the number of students liking football to the number of students liking tennis =
(b) Ratio of the number of students liking cricket to the total number of
students =
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.
Answer:
Number of triangles = 3Number of circles = 2
Number of squares = 2
Total number of figures = 7
(a) Ratio of the number of triangles to the number of circles =
(b) Ratio of the number of squares to all the figures in the rectangle =
(c) Ratio of the number of circles to all the figures in the rectangle =
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.Answer:
The distance travelled in an hour by a certain object is called the speed of that object.Distance travelled by Hamid in one hour = 9 km
Distance travelled by Akhtar in one hour = 12 km
Hamid’s speed = 9 km/hr
Akhtar’s speed = 12 km/hr
Question 5:
Fill in the following blanks:
[Are
these equivalent ratios?]Answer:
Therefore, 5, 12, 25 will come in the blanks respectively.
Yes, all these are equivalent ratios.
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
Answer:
(a)
(b)
(c)
(d)
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 Re1 (d) 500 mL to 2 litres
Answer:
(a) 30 min =
Required ratio =
(b) 40 cm to 1.5 m
1.5 m = 150 cm
Required ratio =
(c) 55 paise to Re 1
Re 1 = 100 paise
Required ratio =
(d) 500 mL to 2l
1l = 1000 mL
2l = 2000 mL
Required ratio =
Question 8:
In a year, Seema earns Rs 1, 50, 000 and saves Rs 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.
Answer:
Money earned = Rs 150000Money saved = Rs 50000
Money spent = Rs 150000 − Rs 50000 = Rs 100000
(a) Ratio of money earned to money saved =
(b) Ratio of money saved to money spent =
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.
Answer:
Total number of students = 4320Number of girls = 2300
Number of boys = 4320 − 2300 = 2020
(a) Required ratio =
(b) Required ratio =
(c) Required ratio =
Page No 252:
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.
Answer:
(a) Required ratio =
(b) Required ratio =
(c) Required ratio =
Q 12 - Ex 12.1 - Ratio and Proportion - NCERT Maths Class 6th - Chapter 12
Question 12:
Cost of a dozen pens is Rs 180 and cost of 8 ball pens is Rs 56. Find the ratio of the cost of a pen to the cost of a ball pen.Answer:
Cost of a dozen pens = Rs 180Cost of 1 pen =
Cost of 8 ball pens = Rs 56
Cost of a ball pen =
Required ratio =
Q 13 - Ex 12.1 - Ratio and Proportion - NCERT Maths Class 6th - Chapter 12
Question 13:
Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the following table that shows some possible breadths and lengths of the hall.
Breadth of the hall (in metres)
|
10
|
?
|
40
|
Length of the hall (in metres)
|
25
|
50
|
?
|
Answer:
(i) Length = 50 m
5 × Breadth = 50 × 2 (By cross-multiplication)
Breadth = 20 m
(ii) Breadth = 40 m
2 × Length = 5 × 40 (By cross-multiplication)
Length = 100 m
Q 14 - Ex 12.1 - Ratio and Proportion - NCERT Maths Class 6th - Chapter 12
Question 14:
Divide 20 pens between Sheela and Sangeeta in the ratio of 3:2.Answer:
Terms of 3 : 2 are 3 and 2.Sum of these terms = 3 + 2 = 5
Sheela will get
of total pens and Sangeeta will get 
of total pens.Number of pens with Sheela =
Number of pens with Sangeeta =
Q 15 - Ex 12.1 - Ratio and Proportion - NCERT Maths Class 6th - Chapter 12
Question 15:
Mother wants to divide Rs 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.Answer:
Ratio of ages =
Therefore, mother wants to divide Rs 36 in a ratio of 5 : 4.
Terms of 5 : 4 are 5 and 4.
Sum of these terms = 5 + 4 = 9
Shreya will get
of the total money and Bhoomika will get 
of it.Amount that Shreya will get =
Amount that Bhoomika will get =
Therefore, Shreya and Bhoomika will get Rs 20 and Rs 16 respectively.
Q 16 - Ex 12.1 - Ratio and Proportion - NCERT Maths Class 6th - Chapter 12
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 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.
Answer:
(a) Present age of father = 42 yearsPresent age of son = 14 years
Required ratio =
(b) Two years ago, the age of the son was 12 years and the age of the father was 42 − 2 = 40 years
Required ratio =
(c) After 10 years, the age of the father and son will be 52 years and 24 years respectively.
Required ratio =
(d) 12 years ago, the father was 30 years old.
At that time, age of son = 14 − 12 = 2 years
Required ratio =
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