3.13 Ratio-to-Percentage Conversion

A ratio a : b can always be converted to percentages by treating (a + b) as the whole (100%):

Percentage share of a = (a)/(a+b) × 100 Percentage share of b = (b)/(a+b) × 100

Worked Example 1: In a class, the ratio of boys to girls is 3 : 2. Find the percentage of boys in the class. Boys% = 3/(3+2) × 100 = 3/5 × 100 = 60%.

Worked Example 2: A mixture contains milk and water in the ratio 4 : 1. What percentage of the mixture is water? Water% = 1/(4+1) × 100 = 1/5 × 100 = 20%.

Worked Example 3: The monthly incomes of A and B are in the ratio 5 : 4, and their monthly expenditures are in the ratio 3 : 2. If A saves 25% of his income, find what percentage of his income B saves (given A’s income = ₹25,000). A’s income = 25,000. Since income ratio is 5:4, B’s income = (4/5) × 25,000 = 20,000. A saves 25% of income, so A’s expenditure = 75% of 25,000 = 18,750. Since expenditure ratio is 3:2, B’s expenditure = (2/3) × 18,750 = 12,500. B’s savings = 20,000 − 12,500 = 7,500. B’s savings% = (7,500/20,000) × 100 = 37.5%. This example shows ratio-to-percentage conversion working alongside percentage-of-income concepts — exactly the kind of composite question SSC CGL Tier-I favours.

Worked Example 4: Two numbers are respectively 25% and 60% more than a third number. What percentage is the first number of the second? Let the third number = x. First number = 1.25x. Second number = 1.60x. First as % of second = (1.25x/1.60x) × 100 = (125/160) × 100 = (25/32) × 100 = 78.125%.

Worked Example 5: The salaries of A and B are in the ratio 7 : 5. If A’s salary is increased by 20% and B’s salary is increased by 40%, find the new ratio of their salaries, and express A’s new salary as a percentage of B’s new salary. Let A = 7k, B = 5k. New A = 7k × 1.20 = 8.4k. New B = 5k × 1.40 = 7k. New ratio = 8.4k : 7k = 8.4 : 7 = 6 : 5 (dividing both by 1.4). A’s new salary as % of B’s new salary = (8.4k/7k) × 100 = 120%.