Proportion and unitary method

Proportion:

If two ratios are equal then we can say that they are in proportion.

Q.1) Person A purchases 2 pens for 6 rupees and person  B purchases 10 pens for 30 rupees. whose pens are more expensive?

sol: 

Pen's ratio = 2:10 = 1:5

Their cost ratio = 6:30 = 1:5

Ratios are the same then we can say that they are in proportion and the cost of pens purchased by them are the same.

Q.2) Determine the following are in proportion (or) not

i) 2,3,30,45

sol: 

30:45 = 2:3

2:3::30:45

ii) 4,6,8,12

sol: 

4:6 = 2:3

8:12 = 2:3

Ratios are equal, they are In proportion.

Q.3) 45 km:60km=12 hrs:15 hrs

sol:

45 km:60km = 3:4

12 hrs:15 hrs = 4:5

Unitary method:

The method in which we find the value of one unit first and then the value of the required number of units is known as the unitary method.

Q.1) If the cost of 3 books is 45 rupees .find the cost of 7 books?

sol: 

Cost of 3 books = 45

cost of 1book = x

$$3 \times x = 1 \times 45$$

3x = 45

x = $$\frac{45}{3} = 15$$

cost of 7 books = 7x = 7 $$\times$$ 15 = 105 rupees.