Introduction to solving proportions:

If two fractions` x/y` and `p/q` are equal, they are said to be in proportion. It can be denoted by x: y :: p: q.

Here the fractions should be of same kind and same unit. The two quantities in a ratio are called its terms. The first term is called antecedent and the second term is called consequent. A ratio
is a pure numbers it has no unit.

In the proportion x: y :: p: q, x and q are called extremes, and y and p are called means

Example Problems on Solving Proportions:

Ex 1. A bottle machine fills 500 bottles in 15 minutes. How many bottles will it fill in `1 1/2` hours?

Sol: Let x be the number of bottles to be filled in `1 1/2` hours = 90 minutes.

Given: `x / 90` = `500 / 15`

`=>` x = `500 xx 90 / 15`

x = 3000 bottles.

Therefore 3000 bottles can be filled in 90 minutes.

Ex 2: A machine prints four books in 10 minutes. How many will it print is 2 hours?

Sol : Let ‘x’ be the number of books need to be printed in 2 hours = 120 minutes.

Given: `x / 120` = `4 / 10`

`=>` x = `4 xx120 / 10` = 48

Therefore 48 books can be printed in 2 hours.

Ex 3: Find the value of x, if 7 : 18 : : x : 27

Sol : Given: 7 : 18 : : x : 27

`=>` ` 7 / 18 = x / 27`

`=>` `18 xx x = 7 xx 27`

Therefore x = `7 xx 27 / 18` = `21 / 2` = 10.5

Ex 4: If x is the mean proportion of 2 and 32, find x?

Sol : Given: 2 : x : : x : 32

`=>` `2/ x = x / 32 `

`=>`` x ^2 = 2 xx 32`

Therefore x 2 = 64

Therefore x = 8.

Ex 5: Find the third proportional to 2 and 32.

Soln: Let x be the third proportional :

We have 2 : 32 = 32 : x

`=>` `2 / 32 = 32 / x`

`=>` 2 x = 32 2

`=>` x =` 32 ^2 / 2` = 512.

If 5 pen costs 8 dollar, what is the cost of 15 pens?

[Ans: 15 pens = 24 dollar]

2. Find the value of x in the proportion 4 : x : : 12 : 9

[Ans : x = 3 ]

3. Find the value of x in 5 : 7 : : 8 : x

[Ans: x = 11.2]