Percentage, Profit-Loss, and Discount
Key Takeaways
- Every percentage question has a base; identifying that base is more important than memorizing a formula.
- Profit and loss percentages are calculated on cost price, while discount is calculated on marked price.
- Successive changes must be compounded, not added, because the second percentage acts on a changed value.
- Markup, discount, and final profit can be solved quickly by assuming a cost price or marked price of 100.
Percent Means Base First
A percentage is a comparison with 100, but the exam trick is the base. In RRB NTPC, the phrase after of, on, more than, less than, profit on, or discount on tells you the base. If the base changes, the answer changes. This is why percentage questions feel simple but produce many wrong attempts.
Use this habit: before calculating, underline the base in your mind. In a salary increase, the old salary is the base. In a discount, marked price is the base. In profit percentage, cost price is the base. In population growth over two years, the second year starts from the changed population, not the original one.
Core Percentage Conversions
| Fraction | Percent | Fast use |
|---|---|---|
| 1/2 | 50% | Half of any value |
| 1/3 | 33.33% | Divide by 3 |
| 1/4 | 25% | Divide by 4 |
| 1/5 | 20% | Divide by 5 |
| 1/8 | 12.5% | Half of 25% |
| 1/10 | 10% | Move one decimal |
Build percentages from easy parts. For 17.5 percent, use 10 percent + 5 percent + 2.5 percent. For 37.5 percent, use 3/8. For 66.66 percent, use 2/3. This is faster and safer than multiplying every time.
Increase, Decrease, and Successive Change
If a value increases by a percent, multiply by 100 + a over 100. If it decreases by a percent, multiply by 100 - a over 100. Two changes are applied one after another. They are not simply added unless the question specifically uses the same original base.
Example method: assume the starting value is 100. A 25 percent increase makes it 125. A 20 percent decrease after that gives 100. The net change is zero, not plus 5 percent. The base shifted after the first step.
For equal rise and fall of x percent, the net result is a loss of x squared divided by 100 percent. This shortcut is useful, but only when the rise and fall are equal and applied successively.
Profit, Loss, and Discount
Cost price is what the seller pays. Selling price is what the buyer pays. Marked price is the listed price before discount. Profit is selling price minus cost price. Loss is cost price minus selling price.
The formula base matters:
| Quantity | Formula base |
|---|---|
| Profit percent | Profit / Cost Price x 100 |
| Loss percent | Loss / Cost Price x 100 |
| Discount percent | Discount / Marked Price x 100 |
| Selling price after discount | Marked Price x (100 - discount%)/100 |
| Marked price after markup | Cost Price x (100 + markup%)/100 |
If cost is not given, assume cost price is 100. If marked price is the base, assume marked price is 100. This removes algebra and keeps the arithmetic visible.
Markup and Discount Together
Shopkeeper questions often combine markup and discount. Do not subtract the percentages directly. A 40 percent markup followed by a 25 percent discount is not automatically a 15 percent profit. Start with cost 100. Marked price becomes 140. Discount of 25 percent on 140 is 35. Selling price is 105, so profit is 5 percent.
A quick multiplier method works well:
- Markup by 30 percent means multiply by 1.30.
- Discount by 10 percent means multiply by 0.90.
- Net selling price factor is 1.30 x 0.90 = 1.17.
- The seller has 17 percent profit on cost.
Use decimals only if you are comfortable with place value. Otherwise keep the same calculation as fractions: 130/100 x 90/100.
Reverse Percentage
Reverse percentage asks for the original value after a change. If a price after 20 percent increase is 600, then 600 represents 120 percent of the original. The original is 600 x 100/120 = 500. Do not subtract 20 percent of 600; that uses the new value as the base.
The same method works for discounts. If a discounted price is 720 after a 10 percent discount, then 720 is 90 percent of marked price. Marked price is 720 x 100/90 = 800. This is a common shopkeeper and bill-value pattern.
Comparing Percentages
A frequent NTPC trap compares two percentages with different bases. If A is 20 percent more than B, then B is not 20 percent less than A. Let B be 100, so A is 120. B is 20 less than 120, which is 16.66 percent less than A.
The same idea appears in population, production, salary, and price questions. When the wording reverses direction, recompute the base. Do not reuse the first percentage.
Exam Strategy
Percentage questions should be quick marks, but only if the base is clear. Spend two seconds identifying the base and one second estimating the range. If the computed result gives profit when the seller sold below cost, or gives a discount larger than marked price, stop and recheck.
Maintain a mini error ledger for percentage topics: wrong base, direct subtraction of successive changes, profit calculated on selling price, discount calculated on cost price, and decimal slip. These five mistakes cause most avoidable losses.
Final Drill Plan
Practice in clusters. First solve pure percentage conversions. Then solve successive changes. Then solve profit-loss. Finally mix markup, discount, and comparison questions. Mixed practice is essential because the actual CBT will not label a question as a base-change trap.
A trader marks goods 50 percent above cost and then gives a 20 percent discount on the marked price. What is the net result?