Aptitude · Lesson 1 of 9

Percentages

Percent basics, fraction shortcuts, increase/decrease and successive changes.

“Per cent” means “out of 100”. Most company aptitude rounds (TCS, Infosys, UST, campus drives) open with percentage questions because they underpin profit, interest and data interpretation.

Key facts

x% of y = x × y / 100 — and x% of y = y% of x (8% of 50 = 50% of 8 = 4).
Fraction shortcuts: 50% = ½, 25% = ¼, 20% = ⅕, 12.5% = ⅛, 33⅓% = ⅓, 16⅔% = ⅙.
Increase by r%: multiply by (1 + r/100). Decrease by r%: multiply by (1 − r/100).
Successive changes a% and b%: net change = a + b + ab/100 (use negative values for decreases).
If A is r% more than B, then B is r/(100 + r) × 100% less than A.

Example: A salary of ₹40,000 is increased by 10% and then reduced by 10%. What is the final salary?

Net change = 10 + (−10) + (10 × −10)/100 = −1%.
Final = 40,000 × 0.99.

Answer: ₹39,600 — a 1% fall, not back to ₹40,000.

Example: Anu's marks are 25% more than Rahul's. By what percent are Rahul's marks less than Anu's?

Use r/(100 + r) × 100 with r = 25.
25/125 × 100 = 20.

Answer: 20% less.

Key points

Convert common percentages to fractions for speed.
Successive change: a + b + ab/100.
‘More than’ and ‘less than’ use different bases.

Quick check

A price rises 20% and then falls 20%. The net change is…

0% 4% decrease 4% increase 2% decrease

Practice task

A town's population of 50,000 grows 10% in year one and 20% in year two. What is it after two years?

Show answer

50,000 × 1.1 × 1.2 = 66,000 (net growth 10 + 20 + 2 = 32%).

Interview corner

How do you find what percent 45 is of 180?

45/180 × 100 = 25%. Spot it faster: 45 is a quarter of 180.

Why isn't a 50% loss recovered by a 50% gain?

The gain is calculated on the smaller amount: 100 → 50 → 75. You need a 100% gain to get back to 100.