RATIO AND PROPORTION
(A) Main Concepts and Results
• Ratio, Proportion and Unitary Method.
• The comparison of two numbers or quantities by division is known
as the ratio. Symbol ‘:’ is used to denote ratio.
• For a ratio, the two quantities must be in the same unit. If they are
not, they should be expressed in the same unit before the ratio is
taken.
• A ratio may be treated as a fraction.
• Two ratios are equivalent, if the fractions corresponding to them
are equivalent.
• Four quantities are said to be in proportion, if the ratio of the first
and the second quantities is equal to the ratio of the third and the
fourth quantities. The symbol ‘::’ or ‘=’ is used to equate the two
ratios.
• The order of terms in a proportion is important. For example 3, 8,
24, 64 are in proportion but 3, 8, 64, 24 are not in proportion.
• The method in which first we find the value of one unit and then the
value of the required number of units is known as unitary method.
Example 1. The ratio of Rs 8 to 80 paise is
(A) 1 : 10 (B) 10 : 1 (C) 1: 1 (D) 100 : 1
Solution: Correct answer is (B)
(Hint: 1 Rupee = 100 paise)
Example 2. The length and breadth of a steel tape are 10m and
2.4cm, respectively. The ratio of the length to the
breadth is
(A) 5 : 1.2 (B) 25: 6 (C) 625: 6 (D) 1250: 3
Solution: Correct answer is (D)
(Hint: 10m = 10 × 100cm)
Example 3. Find the missing number in the box in the following
proportion:
: 8 :: 12 : 32
Solution: 12:32 =
12 3 4 3
3:8
32 8 4 8
We have, : 8 = 3 : 8 (Given)
So, the missing number in is 3.
Example 4. State whether the given statements are true or false:
(a) 12 : 18 = 28 : 56
(b) 25 persons : 130 persons = 15kg : 78kg
Solution: (a) False, Because
12 2
12:18 2:3
18 3
= = =
and
28 1
28:56 1:2
56 2
= = =
These are not equal.
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