Textbook: Ratio & Proportion | Mathematics Class 6 (Maharashtra Board) PDF Download

 Page 3


58
Some Important Points about Ratio
Example : The weight of the large block of jaggery is 1 kg and a smaller lump weighs           
200 g. Find the ratio of the weight of the lump of jaggery to that of the block.
Weight of the lump
Weight of the block
=
200
1
Is this right?
Is the weight of the lump 200 times that of the block?   
What mistake have we made?
First we must measure both quantities in the same units.
 It would be convenient to use grams here.
1kg = 1000 grams
? The block weighs 1000 g and the lump, 200 g.  
Weight of the lump
Weight of the block
 
= 
200
1000
 = 
2 100
10 100
×
×
 = 
2
10
 = 
12
52
×
×
 = 
1
5
Thus, the ratio of the weight of the lump of jaggery to that of the block is 
1
5
.
When finding the ratio of two quantities of the same kind, 
their measures must be in the same units.
 A ratio can be used to write an equation. Then it is easier to solve the problem.  
Example :  A hostel is to be built for schoolgoing girls. Two toilets are to be built for every 
15 girls. If 75 girls will be living in the hostel, how many toilets will be required 
in this proportion?
Let us consider the proportion or ratio of toilets and girls. Let us suppose x 
toilets will be needed for 75 girls. The ratio of the number of toilets to the 
number of girls is 
2
15
.
  
Let us write this in two ways and form an equation.
?
x
75
  = 
2
15
 
? 
x
75
 × 75  = 
2
15
 × 75  (Multiplying both sides by 75)
? x  =  2 × 5 
    = 10     
?
 
10 toilets will be required for 75 girls.
Let’s learn.
Now I know -
Page 4


58
Some Important Points about Ratio
Example : The weight of the large block of jaggery is 1 kg and a smaller lump weighs           
200 g. Find the ratio of the weight of the lump of jaggery to that of the block.
Weight of the lump
Weight of the block
=
200
1
Is this right?
Is the weight of the lump 200 times that of the block?   
What mistake have we made?
First we must measure both quantities in the same units.
 It would be convenient to use grams here.
1kg = 1000 grams
? The block weighs 1000 g and the lump, 200 g.  
Weight of the lump
Weight of the block
 
= 
200
1000
 = 
2 100
10 100
×
×
 = 
2
10
 = 
12
52
×
×
 = 
1
5
Thus, the ratio of the weight of the lump of jaggery to that of the block is 
1
5
.
When finding the ratio of two quantities of the same kind, 
their measures must be in the same units.
 A ratio can be used to write an equation. Then it is easier to solve the problem.  
Example :  A hostel is to be built for schoolgoing girls. Two toilets are to be built for every 
15 girls. If 75 girls will be living in the hostel, how many toilets will be required 
in this proportion?
Let us consider the proportion or ratio of toilets and girls. Let us suppose x 
toilets will be needed for 75 girls. The ratio of the number of toilets to the 
number of girls is 
2
15
.
  
Let us write this in two ways and form an equation.
?
x
75
  = 
2
15
 
? 
x
75
 × 75  = 
2
15
 × 75  (Multiplying both sides by 75)
? x  =  2 × 5 
    = 10     
?
 
10 toilets will be required for 75 girls.
Let’s learn.
Now I know -
59
1. In each example below, find the ratio of the first number to the second.
 (1) 24, 56 (2) 63, 49 (3) 52, 65 (4) 84, 60 (5) 35, 65 (6) 121, 99
2.  Find the ratio of the first quantity to the second.
 (1) 25 beads, 40 beads  (2) 40 rupees, 120 rupees  (3) 15 minutes, 1 hour 
(4) 30 litres, 24 litres (5) 99 kg, 44000 grams  (6) 1 litre, 250 ml
 (7) 60 paise, 1 rupee (8) 750 grams, 
1
2
 kg  (9) 125 cm, 1 metre
3.  Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
4. 30 cricket players and 20 kho- kho players are training on a field. What is the ratio of 
cricket players to the total number of players?
5. Snehal has a red ribbon that is 80 cm long and a blue ribbon, 2.20 m long. What is 
the ratio of the length of the red ribbon to that of the blue ribbon?
6. Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is 
younger than his father by 6 years. Find the following ratios.
 (1) Ratio of Shubham’s age today to his mother’s age today.
 (2) Ratio of Shubham’s mother’s age today to his father’s age today
 (3) The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.
The Unitary Method
 Vijaya wanted to gift pens to seven of her friends on her birthday. When she went to 
a shop to buy them, the shopkeeper told her the rate for a dozen pens. 
?? 	 Can you help Vijaya to find the cost 
of 7 pens?
?? 	 If you find the cost of one pen, you 
can also find the cost of 7, right? 
Practice Set 28
Let’s learn.
A dozen pens 
cost rupees  84.
I want 
7 pens.
Page 5


58
Some Important Points about Ratio
Example : The weight of the large block of jaggery is 1 kg and a smaller lump weighs           
200 g. Find the ratio of the weight of the lump of jaggery to that of the block.
Weight of the lump
Weight of the block
=
200
1
Is this right?
Is the weight of the lump 200 times that of the block?   
What mistake have we made?
First we must measure both quantities in the same units.
 It would be convenient to use grams here.
1kg = 1000 grams
? The block weighs 1000 g and the lump, 200 g.  
Weight of the lump
Weight of the block
 
= 
200
1000
 = 
2 100
10 100
×
×
 = 
2
10
 = 
12
52
×
×
 = 
1
5
Thus, the ratio of the weight of the lump of jaggery to that of the block is 
1
5
.
When finding the ratio of two quantities of the same kind, 
their measures must be in the same units.
 A ratio can be used to write an equation. Then it is easier to solve the problem.  
Example :  A hostel is to be built for schoolgoing girls. Two toilets are to be built for every 
15 girls. If 75 girls will be living in the hostel, how many toilets will be required 
in this proportion?
Let us consider the proportion or ratio of toilets and girls. Let us suppose x 
toilets will be needed for 75 girls. The ratio of the number of toilets to the 
number of girls is 
2
15
.
  
Let us write this in two ways and form an equation.
?
x
75
  = 
2
15
 
? 
x
75
 × 75  = 
2
15
 × 75  (Multiplying both sides by 75)
? x  =  2 × 5 
    = 10     
?
 
10 toilets will be required for 75 girls.
Let’s learn.
Now I know -
59
1. In each example below, find the ratio of the first number to the second.
 (1) 24, 56 (2) 63, 49 (3) 52, 65 (4) 84, 60 (5) 35, 65 (6) 121, 99
2.  Find the ratio of the first quantity to the second.
 (1) 25 beads, 40 beads  (2) 40 rupees, 120 rupees  (3) 15 minutes, 1 hour 
(4) 30 litres, 24 litres (5) 99 kg, 44000 grams  (6) 1 litre, 250 ml
 (7) 60 paise, 1 rupee (8) 750 grams, 
1
2
 kg  (9) 125 cm, 1 metre
3.  Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
4. 30 cricket players and 20 kho- kho players are training on a field. What is the ratio of 
cricket players to the total number of players?
5. Snehal has a red ribbon that is 80 cm long and a blue ribbon, 2.20 m long. What is 
the ratio of the length of the red ribbon to that of the blue ribbon?
6. Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is 
younger than his father by 6 years. Find the following ratios.
 (1) Ratio of Shubham’s age today to his mother’s age today.
 (2) Ratio of Shubham’s mother’s age today to his father’s age today
 (3) The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.
The Unitary Method
 Vijaya wanted to gift pens to seven of her friends on her birthday. When she went to 
a shop to buy them, the shopkeeper told her the rate for a dozen pens. 
?? 	 Can you help Vijaya to find the cost 
of 7 pens?
?? 	 If you find the cost of one pen, you 
can also find the cost of 7, right? 
Practice Set 28
Let’s learn.
A dozen pens 
cost rupees  84.
I want 
7 pens.
60
Example :  A bunch of 15 bananas costs 45 rupees. 
How much will 8 bananas cost?
Cost of 15 bananas, 45 rupees.
         ?  Cost of 1 banana  = 45 ÷ 15 = 3 rupees
Therefore, the cost of 8 bananas is  8 × 3 = 24 rupees
Example : If a bunch of 10 flowers costs 25 rupees, how much will 4 flowers cost?
Cost of 10 flowers, 25 rupees. 
? Cost of 1 flower  = 
25
10
 rupees
Therefore, cost of 4 flowers = 
25
10
 × 4 = 10 rupees.
Find the cost of one article from that of many, by division.
Then find the cost of many articles from that of one, by multiplication.
This method of solving a problem is called the unitary method.
?? Solve the following.
(1) If 20 metres of cloth cost 
` 
3600, find the cost of 16 m of cloth.
(2) Find the cost of 8 kg of rice, if the cost of 10 kg is ` 325.
(3) If 14 chairs cost ` 5992, how much will have to be paid for 12 chairs?
(4) The weight of 30 boxes is 6 kg. What is the weight of 1080 such boxes?
(5) A car travelling at a uniform speed covers a distance of 165 km in 3 hours. At
that same speed, (a) How long will it take to cover a distance of 330 km?
(b) How far will it travel in 8 hours?
(6) A tractor uses up 12 litres of diesel while ploughing 3 acres of land. How much
diesel will be needed to plough 19 acres of land?
(7) At a sugar factory, 5376 kg of sugar can be obtained from 48 tonnes of sugarcane.
If Savitatai has grown 50 tonnes of sugarcane, how much sugar will it yield?
(8) In an orchard, there are 128 mango trees in 8 rows. If all the rows have an equal
number of trees, how many trees would there be in 13 rows?
(9) A pond in a field holds 120000 litres of water. It costs 18000 rupees to make such
a pond. How many ponds will be required to store 480000 litres of water, and
what would be the expense?
?????? Practice Set 29
Now I know -