Selina Textbook Solutions: Ratio | Mathematics Class 6 ICSE PDF Download

 Page 1


IMPORTANT POINTS 
1. Ratio : The relation between two quantities (both of the same kind and in the same 
unit) obtained on dividing one quantity by the other, is called the ratio. 
Keep in Mind : 
(i) The ratio between two numbers or quantities is denoted by the colon “ : ”. 
Thus, the ratio between two quantities p and q = p : q 
(ii) The ratio between two quantities of same kind and in the same units is obtained on 
dividing one quantity by the other. Thus, the ratio between 20 kg and 80 kg =  = 1 
: 4 
(iii) The first term of a ratio is called antecedent and its second term is called 
consequent. In the ratio 1:4; antecendent = 1 and consequent = 4. 
(iv) A ratio must always by expressed in its lowest terms. 
2. Proportion : A proportion is an expression which states that the two ratios are equal. 
Keep in Mind : 
In a proportion, its first and the fourth terms are called extremes whereas its second and 
the third terms are called means. 
Thus, in 8 : 12 = 18 : 27; the terms 12 and 18 are means whereas 8 and 27 are 
extremes. 
Also, Product of extremes = Product of Means 
EXERCISE 11(A) 
Question 1. 
Express each of the following ratios in its simplest form : 
(a) (i) 4 : 6 
(ii) 48 : 54 
(iii) 200 : 250 
(b) (i) 5 kg : 800 gm 
(ii) 30 cm : 2 m 
(iii) 3 m : 90 cm 
(iv) 2 years : 9 months 
(v) 1 hour : 45 minutes 
(vi) 4 min : 45 sec 
Page 2


IMPORTANT POINTS 
1. Ratio : The relation between two quantities (both of the same kind and in the same 
unit) obtained on dividing one quantity by the other, is called the ratio. 
Keep in Mind : 
(i) The ratio between two numbers or quantities is denoted by the colon “ : ”. 
Thus, the ratio between two quantities p and q = p : q 
(ii) The ratio between two quantities of same kind and in the same units is obtained on 
dividing one quantity by the other. Thus, the ratio between 20 kg and 80 kg =  = 1 
: 4 
(iii) The first term of a ratio is called antecedent and its second term is called 
consequent. In the ratio 1:4; antecendent = 1 and consequent = 4. 
(iv) A ratio must always by expressed in its lowest terms. 
2. Proportion : A proportion is an expression which states that the two ratios are equal. 
Keep in Mind : 
In a proportion, its first and the fourth terms are called extremes whereas its second and 
the third terms are called means. 
Thus, in 8 : 12 = 18 : 27; the terms 12 and 18 are means whereas 8 and 27 are 
extremes. 
Also, Product of extremes = Product of Means 
EXERCISE 11(A) 
Question 1. 
Express each of the following ratios in its simplest form : 
(a) (i) 4 : 6 
(ii) 48 : 54 
(iii) 200 : 250 
(b) (i) 5 kg : 800 gm 
(ii) 30 cm : 2 m 
(iii) 3 m : 90 cm 
(iv) 2 years : 9 months 
(v) 1 hour : 45 minutes 
(vi) 4 min : 45 sec 
 
 
Solution: 
Page 3


IMPORTANT POINTS 
1. Ratio : The relation between two quantities (both of the same kind and in the same 
unit) obtained on dividing one quantity by the other, is called the ratio. 
Keep in Mind : 
(i) The ratio between two numbers or quantities is denoted by the colon “ : ”. 
Thus, the ratio between two quantities p and q = p : q 
(ii) The ratio between two quantities of same kind and in the same units is obtained on 
dividing one quantity by the other. Thus, the ratio between 20 kg and 80 kg =  = 1 
: 4 
(iii) The first term of a ratio is called antecedent and its second term is called 
consequent. In the ratio 1:4; antecendent = 1 and consequent = 4. 
(iv) A ratio must always by expressed in its lowest terms. 
2. Proportion : A proportion is an expression which states that the two ratios are equal. 
Keep in Mind : 
In a proportion, its first and the fourth terms are called extremes whereas its second and 
the third terms are called means. 
Thus, in 8 : 12 = 18 : 27; the terms 12 and 18 are means whereas 8 and 27 are 
extremes. 
Also, Product of extremes = Product of Means 
EXERCISE 11(A) 
Question 1. 
Express each of the following ratios in its simplest form : 
(a) (i) 4 : 6 
(ii) 48 : 54 
(iii) 200 : 250 
(b) (i) 5 kg : 800 gm 
(ii) 30 cm : 2 m 
(iii) 3 m : 90 cm 
(iv) 2 years : 9 months 
(v) 1 hour : 45 minutes 
(vi) 4 min : 45 sec 
 
 
Solution: 
 
Question 2. 
A field is 80 m long and 60 m wide. Find the ratio of its width to its length. 
Solution: 
Width of field = 60 m 
Length of field = 80 m 
Ratio between width and length =  = 3 : 4 
Question 3. 
State, true or false : 
(i) A ratio equivalent to 7 : 9 is 27 : 21. 
(ii) A ratio equivalent to 5 : 4 is 240 : 192. 
(iii) A ratio of 250 gm and 3 kg is 1 : 12. 
Solution: 
(i) False. 
Correct: A ratio equivalent to 7 : 9 is 9 : 7 
(ii) True 
(iii) True 
Page 4


IMPORTANT POINTS 
1. Ratio : The relation between two quantities (both of the same kind and in the same 
unit) obtained on dividing one quantity by the other, is called the ratio. 
Keep in Mind : 
(i) The ratio between two numbers or quantities is denoted by the colon “ : ”. 
Thus, the ratio between two quantities p and q = p : q 
(ii) The ratio between two quantities of same kind and in the same units is obtained on 
dividing one quantity by the other. Thus, the ratio between 20 kg and 80 kg =  = 1 
: 4 
(iii) The first term of a ratio is called antecedent and its second term is called 
consequent. In the ratio 1:4; antecendent = 1 and consequent = 4. 
(iv) A ratio must always by expressed in its lowest terms. 
2. Proportion : A proportion is an expression which states that the two ratios are equal. 
Keep in Mind : 
In a proportion, its first and the fourth terms are called extremes whereas its second and 
the third terms are called means. 
Thus, in 8 : 12 = 18 : 27; the terms 12 and 18 are means whereas 8 and 27 are 
extremes. 
Also, Product of extremes = Product of Means 
EXERCISE 11(A) 
Question 1. 
Express each of the following ratios in its simplest form : 
(a) (i) 4 : 6 
(ii) 48 : 54 
(iii) 200 : 250 
(b) (i) 5 kg : 800 gm 
(ii) 30 cm : 2 m 
(iii) 3 m : 90 cm 
(iv) 2 years : 9 months 
(v) 1 hour : 45 minutes 
(vi) 4 min : 45 sec 
 
 
Solution: 
 
Question 2. 
A field is 80 m long and 60 m wide. Find the ratio of its width to its length. 
Solution: 
Width of field = 60 m 
Length of field = 80 m 
Ratio between width and length =  = 3 : 4 
Question 3. 
State, true or false : 
(i) A ratio equivalent to 7 : 9 is 27 : 21. 
(ii) A ratio equivalent to 5 : 4 is 240 : 192. 
(iii) A ratio of 250 gm and 3 kg is 1 : 12. 
Solution: 
(i) False. 
Correct: A ratio equivalent to 7 : 9 is 9 : 7 
(ii) True 
(iii) True 
Question 4. 
Is the ratio of 15 kg and 35 kg same as the ratio of 6 years and 14 years? 
Solution: 
 
Question 5. 
Is the ratio of 6 g and 15 g same as the ratio of 36 cm and 90 cm ? 
Solution: 
 
Question 6. 
Find the ratio between 3.5 m, 475 cm and 2.8 m. 
Solution: 
The given values = 3.5 m, 475 cm and 2.8 m 
= 3.5 x 100 cm : 475 cm : 2.8 x 100 cm 
= 350 cm : 475 cm : 280 cm 
= 70 cm : 95 cm : 56 cm 
The ratio is 70 : 95 : 56 
Question 7. 
Find the ratio between 5 dozen and 2 scores. [1 score = 20] 
Solution: 
Ratio between 5 dozen and 2 scores 
Given = 1 score = 20 
then, 2 scores = 2 x 20 = 40 
Page 5


IMPORTANT POINTS 
1. Ratio : The relation between two quantities (both of the same kind and in the same 
unit) obtained on dividing one quantity by the other, is called the ratio. 
Keep in Mind : 
(i) The ratio between two numbers or quantities is denoted by the colon “ : ”. 
Thus, the ratio between two quantities p and q = p : q 
(ii) The ratio between two quantities of same kind and in the same units is obtained on 
dividing one quantity by the other. Thus, the ratio between 20 kg and 80 kg =  = 1 
: 4 
(iii) The first term of a ratio is called antecedent and its second term is called 
consequent. In the ratio 1:4; antecendent = 1 and consequent = 4. 
(iv) A ratio must always by expressed in its lowest terms. 
2. Proportion : A proportion is an expression which states that the two ratios are equal. 
Keep in Mind : 
In a proportion, its first and the fourth terms are called extremes whereas its second and 
the third terms are called means. 
Thus, in 8 : 12 = 18 : 27; the terms 12 and 18 are means whereas 8 and 27 are 
extremes. 
Also, Product of extremes = Product of Means 
EXERCISE 11(A) 
Question 1. 
Express each of the following ratios in its simplest form : 
(a) (i) 4 : 6 
(ii) 48 : 54 
(iii) 200 : 250 
(b) (i) 5 kg : 800 gm 
(ii) 30 cm : 2 m 
(iii) 3 m : 90 cm 
(iv) 2 years : 9 months 
(v) 1 hour : 45 minutes 
(vi) 4 min : 45 sec 
 
 
Solution: 
 
Question 2. 
A field is 80 m long and 60 m wide. Find the ratio of its width to its length. 
Solution: 
Width of field = 60 m 
Length of field = 80 m 
Ratio between width and length =  = 3 : 4 
Question 3. 
State, true or false : 
(i) A ratio equivalent to 7 : 9 is 27 : 21. 
(ii) A ratio equivalent to 5 : 4 is 240 : 192. 
(iii) A ratio of 250 gm and 3 kg is 1 : 12. 
Solution: 
(i) False. 
Correct: A ratio equivalent to 7 : 9 is 9 : 7 
(ii) True 
(iii) True 
Question 4. 
Is the ratio of 15 kg and 35 kg same as the ratio of 6 years and 14 years? 
Solution: 
 
Question 5. 
Is the ratio of 6 g and 15 g same as the ratio of 36 cm and 90 cm ? 
Solution: 
 
Question 6. 
Find the ratio between 3.5 m, 475 cm and 2.8 m. 
Solution: 
The given values = 3.5 m, 475 cm and 2.8 m 
= 3.5 x 100 cm : 475 cm : 2.8 x 100 cm 
= 350 cm : 475 cm : 280 cm 
= 70 cm : 95 cm : 56 cm 
The ratio is 70 : 95 : 56 
Question 7. 
Find the ratio between 5 dozen and 2 scores. [1 score = 20] 
Solution: 
Ratio between 5 dozen and 2 scores 
Given = 1 score = 20 
then, 2 scores = 2 x 20 = 40 
and 1 dozen = 12, 
5 dozen = 12 x 5 = 60 
Then, ratio = 60 : 40 = 3 : 2 
EXERCISE 11(B) 
Question 1. 
The monthly salary of a person is Rs. 12,000 and his monthly expenditure is Rs 8,500. 
Find the ratio of his: 
(i) salary to expenditure 
(ii) expenditure to savings 
(ii) savings to salary 
Solution: 
Monthly salary of a person = Rs 12,000 
Monthly expenditure = 8,500 
Saving of the person = (12,000 – 8500) = Rs 3,500 
 
Question 2. 
The strength of a class is 65, including 30 girls. Find the ratio of the number of: 
(i) girls to boys 
(ii) boys to the whole class 
(iii) the whole class to girls. 
Solution: 
Total strength of class (including boys and girls) = 65 
Number of girls = 30 
Number of boys = (65 – 30) = 35