Percentage, Profit and Loss, and Discount Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
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Percentage, profit and loss, and discount make a large part of every SSC maths paper, and all of them use the same few ideas. This percentage, profit and loss, and discount formula guide for SSC gives the fraction table, the formulas of percentage change, the profit and loss formulas, the marked price formulas and the special shortcuts, with solved examples.
Fraction and Percentage Table
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/9 | 11.11% |
| 1/3 | 33.33% | 1/10 | 10% |
| 1/4 | 25% | 1/11 | 9.09% |
| 1/5 | 20% | 1/12 | 8.33% |
| 1/6 | 16.67% | 1/15 | 6.67% |
| 1/7 | 14.28% | 1/16 | 6.25% |
| 1/8 | 12.5% | 1/20 | 5% |
Percentage Formulas
| Item | Formula |
|---|---|
| Percentage | (Part / Whole) × 100 |
| x% of y | x% of y = y% of x |
| New value after an increase of r% | Old value × (100 + r) / 100 |
| New value after a decrease of r% | Old value × (100 − r) / 100 |
| Two successive changes of a% and b% | Net change = a + b + ab/100 (use a minus sign for a decrease) |
| Increase of r% followed by a decrease of r% | Net decrease = r²/100 % |
| If A is x% more than B | B is [x / (100 + x)] × 100 % less than A |
| If A is x% less than B | B is [x / (100 − x)] × 100 % more than A |
| If the price rises by x% | Consumption must decrease by [x / (100 + x)] × 100 % to keep the expense the same |
| If the price falls by x% | Consumption must increase by [x / (100 − x)] × 100 % |
| Population growth in n years at r% | P × (1 + r/100)^n |
Profit and Loss Formulas
| Item | Formula |
|---|---|
| Profit and loss | Profit = SP − CP; Loss = CP − SP |
| Profit % | (Profit / CP) × 100 |
| Loss % | (Loss / CP) × 100 |
| Selling price | SP = CP × (100 + Profit %) / 100, or CP × (100 − Loss %) / 100 |
| Cost price | CP = SP × 100 / (100 + Profit %), or SP × 100 / (100 − Loss %) |
| Two articles sold at the same price, one at p% profit and the other at p% loss | Net loss = p²/100 % |
| CP of x articles = SP of y articles | Profit % = [(x − y) / y] × 100 |
| False weight | Profit % = [Error / (True weight − Error)] × 100 |
Discount and Marked Price
| Item | Formula |
|---|---|
| Discount | Marked price (MP) − Selling price (SP) |
| Discount % | (Discount / MP) × 100 |
| SP after a discount of d% | MP × (100 − d) / 100 |
| Two successive discounts a% and b% | Single discount = a + b − ab/100 |
| Marked up by x% and a discount of y% | Net profit (or loss) % = x − y − xy/100 |
| MP for a given profit and discount | MP = CP × (100 + Profit %) / (100 − Discount %) |
Discount is always on the marked price, while profit and loss are always on the cost price, unless the question says something else.
Solved Examples
Example 1. The price of sugar increases by 25%. By what percentage must a family reduce its consumption so that the expense stays the same?
[25 / (100 + 25)] × 100 = 20%.
Example 2. The cost price of an article is 500 rupees and the selling price is 575 rupees. Find the profit %.
Profit = 75, and profit % = (75 / 500) × 100 = 15%.
Example 3. The cost price of 15 articles is equal to the selling price of 12 articles. Find the profit %.
[(15 − 12) / 12] × 100 = 25%.
Example 4. A shopkeeper marks the goods 25% above the cost price and gives a discount of 20%. Find his profit or loss %.
25 − 20 − (25 × 20)/100 = 5 − 5 = 0, so there is no profit and no loss.
Example 5. Find the single discount equal to successive discounts of 20% and 10%.
20 + 10 − (20 × 10)/100 = 30 − 2 = 28%.
Example 6. The population of a town is 10,000 and it grows at 10% a year. Find the population after 2 years.
10,000 × 1.1 × 1.1 = 12,100.
Quick Tips
- Learn the fraction and percentage table, because it turns many questions into one-line answers.
- Always check whether the percentage is on the cost price or on the marked price.
- Use successive change formulas instead of two separate calculations.
- Remember the special shortcuts: same SP with equal profit and loss gives a loss of p²/100 %.
Quick Revision Points
- Profit % = (Profit / CP) × 100.
- Successive change = a + b + ab/100.
- Discount % is on the marked price.
- Net loss with the same SP and equal profit and loss % = p²/100 %.
- The CP of x articles equal to the SP of y articles gives a profit % of (x − y)/y × 100.
Practice Questions With Answers
- Find 20% of 250.
Answer: 50 - Increase 40 by 25%.
Answer: 50 - The price of sugar goes up by 20%. By how much % must the consumption be reduced to keep the expense the same?
Answer: 16.67% (that is 16 and 2/3 %) - The cost price is 400 rupees and the selling price is 500 rupees. Find the profit %.
Answer: 25% - The marked price is 1000 rupees and the discount is 10%. Find the selling price.
Answer: 900 rupees - Find the single discount equal to two successive discounts of 10% and 10%.
Answer: 19% - The cost price is 800 rupees and the loss is 5%. Find the selling price.
Answer: 760 rupees - Two articles are sold at the same price, one at a 10% profit and the other at a 10% loss. Find the net result.
Answer: A loss of 1% - A is 25% more than B. By what % is B less than A?
Answer: 20% - A trader uses a weight of 800 g in place of 1 kg. Find his profit %.
Answer: 25%
How to Practise This Chapter
Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The previous guide is Number System, HCF and LCM, the Arithmetic Formula Guide has the interest formulas, and the next guide is Ratio, Proportion, Mixture and Partnership.
Frequently Asked Questions
What is the formula for percentage?
Percentage is the part divided by the whole, multiplied by 100.
What is the formula for profit percentage?
Profit percentage is the profit divided by the cost price, multiplied by 100.
On which price is the discount calculated?
The discount is calculated on the marked price.
What is the formula for two successive discounts?
The single discount is a + b minus ab/100.
What is the net result when the same SP gives a profit and a loss of p%?
There is a loss of p squared divided by 100 percent.
What is the formula for a dishonest dealer who uses a false weight?
Profit % = error divided by (true weight minus error), multiplied by 100.
How do I find the reduction in consumption when the price rises?
Use x/(100 + x) times 100 percent, where x is the price rise.
What is the formula for the selling price with a given profit?
SP = CP times (100 + profit %) divided by 100.
What is the marked price formula?
MP = CP times (100 + profit %) divided by (100 minus discount %).
Why should I learn the fraction and percentage table?
It converts many percentage questions into simple fractions, which saves a lot of time.
Is this topic asked in SSC exams?
Yes. Percentage, profit and loss, and discount questions are asked in every SSC maths paper.
How many questions come from this topic in SSC exams?
Usually four to eight questions, including the data-based ones, but the number changes from exam to exam.
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Number System, HCF and LCM Formula Guide for SSC Exams
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Ratio, Proportion, Mixture and Partnership Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.