Page 94 - ICSE Math 7

Example 4: Which of the following ratios is the greatest?
1 5 2
3 : 8, : 4 or :
2 6 3
1
Solution: Converting ratio : 4 into its simplest form.
2
1  1 
: 4 =  × 2 : (4 × 2) = 1 : 8 (LCM of 2 and 1 = 2)

2  2 
5
2
Converting ratio : into its simplest form.
6 3
5 2  5   2 
: =  × 6 :  × 6 = 5 : 4 (LCM of 6 and 3 = 6)


6 3  6   3 
Thus, the three ratios are 3 : 8, 1 : 8 and 5 : 4.
The LCM of 8, 8 and 4 is 8.
5 × 2 10
∴ 5 : 4 = = = 10 : 8 (Q 8 ÷ 4 = 2)
4 × 2 8
Therefore, the three ratios are 3 : 8, 1 : 8 and 10 : 8.
5 2
As, 10 > 3 > 1, thus, 10 : 8, i.e., : is the greatest.
6 3
Compound ratio
A ratio is known as the compound ratio of two or more ratios if its antecedent is the product of the
antecedents of the given ratios and its consequent is the product of the consequents of the given ratios.
So, the compound ratio of a : b and c : d is ac : bd.
For example, the compound ratio of 3 : 5 and 2 : 7 is (3 × 2) : (5 × 7) = 6 : 35.
1 3
Example 5: Find the compound ratio of 7 : 3 and : .
5 10
1 3  1   3 
Solution: : =  × 10 :  × 10 = 2 : 3 (LCM of 5 and 10 = 10)


5 10  5   10 
∴ Required compound ratio = (7 × 2) : (3 × 3) = 14 : 9
Continued ratio
Three quantities a, b and c are said to be in continued ratio if the ratio of the first two quantities is a : b
and the ratio of the last two quantities is b : c. It is denoted by a : b : c. It is used to compare three
quantities of the same kind. For example, if p : q = 21 : 25 and q : r = 25 : 27, then p, q and r are in
continued ratio and it is written as 21 : 25 : 27.

Increase or decrease in a given ratio
Suppose the price of an article is increased from ` 20 to ` 25.

Ratio of old price to new price = ` 20 : ` 25 = 4 : 5. So, the price has increased in the ratio 4 : 5.
Old price 4
As, =
New price 5
5
∴ New price = × Old price
4
Thus, if the ratio of original quantity to final quantity is a : b, then
b
Final quantity = × Original quantity
a
The ratio by which the original quantity is multiplied to get the final (increased or decreased) quantity
is known as multiplying ratio or factor.

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