Cat Quantitative Ability Percentages Handwritten Notes

CAT Percentages handwritten notes, free to download as a 22-page PDF with 12 solved questions. Percentages feed about 6 to 10 marks across Quant and DI.

Percentages rarely arrive as a labelled question. They sit inside profit and loss, interest, mixtures and most Data Interpretation sets, so the payoff from this topic is larger than its question count suggests.

Why the Base Matters More Than the Number

A percentage on its own means nothing. Almost every wrong answer in this topic uses the right arithmetic on the wrong base.

A price moving 80 to 100 is a 25 per cent rise. The same 20 rupees coming back off 100 is a 20 per cent fall. Nothing changed but the denominator.

• Write every change as a multiplying factor, not as an addition
• Measure change against the original value
• Say the base out loud before starting: percent of what?

The Fraction Table Does Most of the Work

The notes open with the fraction equivalents because they turn long multiplications into one line of mental arithmetic.

• 37.5 per cent is 3/8, so 37.5 per cent of 216 is 81
• 16.67 per cent is 1/6, so a division replaces a multiplication
• x per cent of y always equals y per cent of x
• Awkward percentages split: 35 per cent is 25 plus 10

Successive Changes and Product Constancy

Percentages never add. Up 20 then down 20 leaves 0.96 of the original, a 4 per cent loss, because the rise is taken on the smaller number and the fall on the larger.

The same idea gives product constancy. When price times quantity is fixed, a rise of 1/n forces a fall of 1/(n plus 1).

• Price up 25 per cent means consumption down 20 per cent
• Net of two changes is x plus y plus xy/100, signs included
• The same rule covers area when both sides change
• It also drives speed and time, and men and days

The Question Shapes CAT Repeats

Four shapes come back year after year, and the notes work each one on numbers rather than symbols.

• Passing marks: two candidates describe the same pass mark
• Elections: the margin is twice the winner's share minus 100
• Income and savings: two of the three quantities fix the third
• Mixtures: the pure component stays fixed while water moves

When no figure is given, set the base to 100. Percentages become rupees and the arithmetic collapses to one line.

Watch Percentage Shortcuts Worked Out

Source: Rodha

Where Students Lose Marks Here

Each of these is marked in the notes with the correction written beside it.

• Adding successive percentages instead of multiplying the factors
• Assuming up x then down x returns to the start
• Treating x per cent more and x per cent less as mirror images
• Subtracting to reverse a rise instead of dividing by the factor
• Confusing a percentage point with a percentage change
• Taking discount on cost price, or profit on marked price

How to Use These Notes Before the Exam

The fraction table and the quick recall page are the two to revisit. Everything else exists to explain them.

• Assume 100 whenever no actual figure is given
• Convert percentages to fractions before multiplying
• Underline the quantity the question actually asks for
• Do the twelve solved questions closed book, then check the working

If a percentage question is taking more than ninety seconds, the base was never fixed. That single check saves more time than any shortcut.