Percentage Basics and Fast Conversions

Percentage is the engine of the whole Numerical section — profit and loss, interest, data interpretation and ratio all run on it, so the seconds you save here multiply across the paper. The single highest-return skill is converting a percentage into a fraction instantly, because a fraction turns an ugly multiplication into a one-step division. In SBI Clerk this block itself gives three to five direct questions, and the conversions quietly speed up dozens more.

The Percentage-Fraction Table

Memorise the common percentage-to-fraction pairs so that a figure like 37.5% becomes 3/8 on sight. Finding 37.5% of 4,800 is then just 4,800 × 3/8 = 1,800 in a single mental step, with no decimal multiplication at all. Every value below repeats endlessly in the exam, so treating this table as reflex — not something you derive each time — is what separates a fast candidate from a slow one.

Percentage Increase and Decrease

An increase of x% multiplies a value by (100 + x)/100, and a decrease multiplies it by (100 − x)/100, so a 20% rise on 250 is 250 × 120/100 = 300 without adding anything separately. Reading the change as a single multiplier is faster and far less error-prone than finding the change and adding it back. This one habit removes most careless slips in percentage questions and sets up interest and profit sums cleanly. The same multiplier idea answers the common 'by what percent is A more or less than B' question: A is more than B by (A − B)/B × 100, and B is less than A by (A − B)/A × 100 — the base in the denominator decides the answer, which is why the two figures differ even for the same pair of numbers.

Increase by x%: value × (100 + x)/100 Decrease by x%: value × (100 − x)/100

Solved Examples

Example 1: 62.5% of 3,200 = 3,200 × 5/8 = 2,000, because 62.5% is 5/8 — no decimal work. Example 2: A salary of 40,000 cut by 15% becomes 40,000 × 85/100 = 34,000 in one step. Example 3: If 45 is 15% of a number, the number is 45 × 100/15 = 300, so divide by the percentage and multiply by 100. Example 4: Comparing values, if A is 25% more than B, then B is only 20% less than A, because the base flips from B to the larger A — a difference the exam tests constantly.

✗ Finding 15% of 40,000 then subtracting separately  |  ✓ Multiplying 40,000 by 85/100 in one step

Introduction to Successive Change

When a value changes twice — say a 10% rise followed by a 10% fall — the two percentages do not cancel, because the second acts on a new base. Multiply the two factors instead: 1.10 × 0.90 = 0.99, a net 1% fall. This multiplier chain is the seed of the successive-change formula in the last topic and shows why 'increase then equal decrease' always ends slightly below the start, never back at it. Reading every percentage question as a chain of multipliers, rather than a series of add-and-subtract steps, is the single mindset that keeps this section fast, and it carries directly into profit, interest and data interpretation.