Percentages are the most fundamental topic in CAT Arithmetic, forming the base for Profit & Loss, Simple & Compound Interest, and Data Interpretation. This guided path will teach you the core concepts and advanced shortcuts needed to solve these problems with speed and accuracy.
Start with the basics: converting between percents and fractions, and mastering the three core problems (finding the part, percent, or whole).
Convert any fraction to a percentage.
Memorize and practice using fractional multipliers for common percent increases and decreases. This is a critical speed-boosting technique for the CAT.
| Percent Change | Multiplier |
|---|---|
| 16.66% | $$ 7/6 $$ |
| 20% | $$ 6/5 $$ |
| 25% | $$ 5/4 $$ |
| 33.33% | $$ 4/3 $$ |
| 50% | $$ 3/2 $$ |
| 100% | $$ 2 $$ |
Memorize the multipliers for decreases.
| Percent Change | Multiplier |
|---|---|
| 16.66% | $$ 5/6 $$ |
| 20% | $$ 4/5 $$ |
| 25% | $$ 3/4 $$ |
| 33.33% | $$ 2/3 $$ |
| 50% | $$ 1/2 $$ |
Understand the principle of "growth on growth." This visualizer is the key to mastering both compound interest and successive percent changes.
Compounding means growth is calculated on the new, larger base, not the original.
Example: Invest $100 at 10% annual growth.
$$ 100 + (10\% \text{ of } 100) = 100 + 10 = \$110 $$
Growth: $10
Now we calculate 10% of the NEW base ($110).
$$ 110 + (10\% \text{ of } 110) = 110 + 11 = \$121 $$
Growth: $11 (More than Year 1!)
This is "Interest on Interest". This same logic applies to successive percent changes in GMAT/GRE problems.
The CAT loves this trap. Use our interactive demo to see why a +X% and a -X% change don't cancel out, and learn the logic to solve these problems quickly.
+ 20% and - 20%
= 0% change
$100 → +20% → $120.00
$120.00 → -20% → $96.00
The +20% increase adds $20. The -20% decrease is on the NEW, larger value ($120), so it subtracts $24.00. Result < Start.
Now that you understand the trap, learn the specific formulas required to perfectly reverse an initial percent increase or decrease.
Select a scenario to see the exact percentage needed to return to the original value.
Learn the fundamental vocabulary of Profit & Loss and the relationship between Cost Price, Markup, and Selling Price.
This is the price a seller pays. Example: Shopkeeper buys a shirt for $80.
Seller adds a 50% Markup.
$$ MP = 80 + (50\% \text{ of } 80) = 80 + 40 = \$120 $$
Seller offers 10% Discount on MP.
$$ SP = 120 - (10\% \text{ of } 120) = 120 - 12 = \$108 $$
Profit is always calculated on original CP ($80).
$$ \text{Profit} = 108 - 80 = \$28 $$
$$ \% \text{Profit} = \frac{28}{80} \times 100 = 35\% $$
Tackle classic CAT problems involving successive discounts, finding overall profit/loss after multiple sales, and scenarios with faulty weights.
Item marked up 50%, then two discounts: 20% and 10%. Find Profit %.
Let CP = $100
MP = $150
Discount on $150.
$$ 150 \times 0.8 = \$120 $$
Discount on NEW price ($120).
$$ 120 \times 0.9 = \$108 $$
Final SP = $108. CP = $100.
Profit = 8%
Put your understanding of CAT Percentages, Profit & Loss: A Strategic Guide to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
Stop calculating! Learn how to use the properties of symmetry to solve hard SD questions in seconds.
Forget formulas for a moment. Learn the 'Systematic Listing' method to build an unshakable intuition for Permutations & Combinations.
How to use 'Extreme Values' to find the range of a sum without calculating every fraction.