Percentages

Percent means "per hundred". Writing 25% is the same as writing 25/100, or 0.25.

Three questions cover almost every percentage sum in MPSC prelims:

1. What is x% of N? → multiply: N × x/100
2. A is what percent of B? → divide, then scale: (A/B) × 100
3. N increases/decreases by x% → N × (100 ± x)/100

The single most common mistake is answering question 2 with question 1's method. Read which quantity is the whole: it is the number that follows "of".

Fractions worth memorising — they turn a 40-second sum into a 5-second one:

1/2 = 50%, 1/3 = 33⅓%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/20 = 5%.

x% of N = N × x/100 · A as % of B = (A/B) × 100 · Successive change = a + b + ab/100

45 is what percent of 180? → This is type 2. (45/180) × 100 = 0.25 × 100 = 25%. Sanity check: 45 is a quarter of 180, and a quarter is 25%.