Page 91 - ICSE Math 8

Example 1: Which ratio is greater—5 : 9 or 12 : 17?
5 17 85 12 9 108
Solution: × = and × = ( LCM of 9 and 17 = 153)
9 17 153 17 9 153
85 108
As < , therefore 12 : 17 > 5 : 9.
153 153

Dividing a Quantity in a Given Ratio

We can divide a quantity into parts that are in a particular ratio to each other.
Dividing into two parts
Suppose a quantity a is to be divided in the ratio x : y, then
 x   y 
First part =   × a and Second part =   × a
 x + y   x + y 

Dividing into three parts
If quantity a is to be divided in the ratio x : y : z, then

 x   y   z 
First part =   × a, Second part =   × a and Third part =   × a
 x + yz+   x + yz+   x + yz+ 

Example 2: A shopkeeper had 640 fruits (apples and oranges) in the ratio 5 : 3. He sold 100 apples and
some oranges and the ratio changed to 3 : 2. Find the number of oranges sold.
5
Solution: Number of apples present initially = × 640 = 400
5 + 3
3
Number of oranges present initially = × 640 = 240
5 + 3
Let the number of oranges sold be x. ∴ Number of oranges left = 240 – x
Number of apples sold = 100 ∴ Number of apples left = 400 – 100 = 300
According to the question,
300 3
= ⇒ 600 = 720 – 3x ⇒ 3x = 120 ⇒ x = 40
240 – x 2
∴ 40 oranges were sold.

Example 3: In a piggy bank, there are three types of coins (` 2, ` 1 and ` 5). The total amount in the piggy
bank is ` 140. If the ratio of the total values of the three types of coins is 10 : 15 : 3, find the
number of coins of each type.
10 10
Solution: Total value of ` 2 coins = 10 + 15 + 3 × ` 140 = 28 × ` 140 = ` 50

50
∴ Number of ` 2 coins = 2 = 25

15 15
Total value of ` 1 coins = 10 + 15 + 3 × ` 140 = 28 × ` 140 = ` 75

75
∴ Number of ` 1 coins = 1 = 75
3 3
Total value of ` 5 coins = × ` 140 = × ` 140 = ` 15
10 + 15 + 3 28

15
∴ Number of ` 5 coins = = 3
5

79