Page 43 - Arithmetic

Ratio and Proportion Ratio
Ratio is when two different quantities are compared. For example, if a farmer grows 4 oranges and 5 apples, the ratio of orange to apple is 4:5. When the expression is written in the fraction term, it’s called
4 a ratio. In the above example, the ratio is 5.
Proportion
The equation of two ratios is called a proportion. For example, if p:q = r:s, the proportion is p:q :: r:s where p, q, r, and s are real numbers.
p and s are called the extreme terms
q and r are called the mean terms.
REMEMBER:
Product of mean terms = Product of extreme terms
(p × s) = (q × r)
Important points to remember:
x is directly proportional of y, if x =ay for some constant a, then x ∝ y
x is inversely proportional of y, if xy =a for some constant a, then x ∝ 𝟏 𝒚
Worked Example 18
The salaries of three best friends are in the ratio of 1:2:3. If each of them receives an increment of 5%, 10%, and 15% respectively, what will be the new ratios?
Solution:
Let the salaries of the three friends be x, 2x, and 3x. New salary of the first friend = 105x =21 x
100 20
New salary of the second friend = 110 × 2x = 44 x 100 20
New salary of the third friend = 115 × 3x = 69 x 100 20
New ratio of the salaries = 21 x: 44 x: = 69 x 20 20 20
= 21:44:69
Page 42 of 55
Arithmetic Concept