If A's salary is 20% more than B's, by what percentage is B's salary less than A's?
B's salary is 16.67% (1/6) less than A's. If B earns 100, A earns 120. The gap of 20 is measured against A's 120: 20/120 = 1/6 = 16.67%.
Explain it simply
A percentage is always "out of" something, and the something changes depending on who you compare against. Saying A is 20% more than B uses B as the base. Saying B is less than A uses A as the base. The rupee gap is the same, but it is divided by a bigger number, so the percentage is smaller.
Example
Question: A earns 20% more than B. By what percent is B's salary less than A's?
- Let B = ₹30,000. Then A = 30,000 x 1.2 = ₹36,000.
- Gap = ₹6,000.
- As a percentage of A: 6,000 / 36,000 x 100 = 16.67% (exactly 16 2/3 %).
Shortcut: if A is r% more than B, then B is r / (100 + r) x 100 % less than A. If A is r% less than B, then B is r / (100 - r) x 100 % more than A.
Remembering fraction equivalents helps: 20% = 1/5, so A = 6/5 of B and B = 5/6 of A, which is 1/6 less.
console.log(((36000 - 30000) / 36000 * 100).toFixed(2)); // Output: 16.67What to say in the interview
"The base flips. With B as 100, A is 120, and B is 20 less out of 120, so 16 and two thirds percent less. The quick formula is r over 100 plus r."
Common mistakes
- Answering 20% for both directions.
- Dividing by the smaller salary when the question asks how much less.