Profit and Loss is among the highest-yield areas in AFCAT Numerical Ability — almost every paper carries one or two direct questions, and the idea also feeds Percentage, Discount and Partnership sums. The whole topic rests on the link between cost price, selling price and percentage. This Cavalier guide builds each rule from scratch and hands you the speed tricks that save real seconds in the exam hall.
Why Profit and Loss is a must-score topic
Profit and Loss is simply the arithmetic of buying and selling. You buy something at a cost price (CP) and sell it at a selling price (SP); if SP is higher you gain, if it is lower you lose. Examiners love the topic because the idea is everyday and intuitive, yet the same numbers can be dressed up as shopkeepers, traders, discounts or dishonest dealers.
For AFCAT, this chapter overlaps heavily with Percentage, Ratio and Mixtures, so the effort you put in here pays off across the whole Numerical Ability section. Most questions are one-step or two-step once you fix what is being asked for.
At The Cavalier we tell our defence aspirants to treat Profit and Loss as a guaranteed scoring booster: the data is friendly and a calm reader rarely loses marks here. The only enemies are careless percentage arithmetic and reading the question in a hurry — especially confusing whether a percent is taken on CP or on SP.
Unless the question says otherwise, profit% and loss% are always calculated on the cost price, never on the selling price. This single habit prevents the most common error in the whole chapter.
The core terms: CP, SP, profit and loss
Everything in this topic flows from four quantities. Get these crystal clear before touching formulas.
- Cost Price (CP) = price at which an article is bought.
- Selling Price (SP) = price at which it is sold.
- Profit (Gain) = SP − CP, when SP > CP.
- Loss = CP − SP, when CP > SP.
From these come the two headline formulas examiners test most:
Profit% = (Profit ÷ CP) × 100
Loss% = (Loss ÷ CP) × 100
Always ask: which quantity is unknown? If you know CP and SP, you want profit or loss. If you know CP and profit%, you want SP. Identifying the missing piece before you calculate stops you solving the wrong thing under exam pressure.
It also helps to picture why the formula works. Profit and loss measure how far the selling price has moved away from what you paid, expressed as a fraction of that original cost. Because the cost price is your reference point, the same rupee gain looks like a bigger percentage on a cheap item and a smaller percentage on an expensive one. Keeping the cost price firmly as the base is what makes every later shortcut in this chapter reliable, so train your eye to spot the CP first in every question before you decide what to do with the other numbers.
An article is bought for ₹400 and sold for ₹480. Find the profit percent.
The multiplying-factor shortcut for SP and CP
The slowest way to find SP is to compute profit separately and add it. The fast way is a single multiplying factor.
SP = CP × (100 + Profit%) ÷ 100
SP = CP × (100 − Loss%) ÷ 100
And in reverse: CP = SP × 100 ÷ (100 ± Profit/Loss%).
Turn the percent into a factor and multiply in one step. A 25% profit means SP = 1.25 × CP; a 10% loss means SP = 0.90 × CP. No addition needed.
A trader sells a fan at 15% profit for ₹1,725. Find the cost price.
To back-find CP from SP, divide by 1.15 — do not simply take 15% of the SP and subtract. That gives a slightly wrong CP because the 15% was on CP, not on SP.
The multiplying-factor habit is one of the biggest time-savers in the whole Numerical Ability paper. Once you stop thinking in terms of “find the profit, then add it” and start thinking in terms of a single factor like 1.15 or 0.88, two-step questions collapse into one quick multiplication. It also chains beautifully: if goods are first marked up and then discounted, you simply multiply the two factors together. Practise converting common percentages to factors — 5% is 1.05, 12.5% is 1.125, 8% loss is 0.92 — until the conversion is instant.
Marked price, discount and selling price
Shopkeepers print a Marked Price (MP) — also called list price or tag price — then offer a discount on it. Discount is always taken on MP.
Discount = MP − SP
Discount% = (Discount ÷ MP) × 100
SP = MP × (100 − Discount%) ÷ 100
The chain to keep in mind is CP → MP → SP. The seller marks the goods above cost, then a discount brings the marked price down to the actual selling price. Profit or loss is still judged on CP at the end.
A shirt marked at ₹1,200 is sold after a 20% discount. Find the selling price.
Discount% is on the marked price; profit% is on the cost price. Mixing the two bases is the single biggest trap in discount questions.
A useful way to read these problems is to follow the money in order. The trader starts from a cost price, decides on a markup to set the marked price, then sacrifices some of that markup as a discount to attract the buyer. Whatever is left after the discount is the selling price, and the gap between selling price and cost price is the real profit. Many AFCAT questions deliberately give you three of these four figures and ask for the fourth, so being comfortable moving up and down the CP-MP-SP chain is exactly the skill being tested.
Successive discounts and percentage changes
When two discounts are given one after another (say 20% then 10%), you cannot add them to 30%. The second discount applies to the already-reduced price.
Net effect of two changes a% and b% = a + b + (a × b) ÷ 100.
For discounts, both a and b are negative.
Two successive discounts of 20% and 10%: net = −20 −10 + (−20 × −10)÷100 = −30 + 2 = −28%. So a single equivalent discount of 28%, not 30%.
An item marked ₹2,000 carries successive discounts of 25% and 20%. Find the final price.
Adding 25% + 20% = 45% discount is wrong. The correct equivalent is 40%, because the second cut is on the smaller, post-first-discount amount.
The same successive-percentage formula handles a markup followed by a discount, or a price that first rises and then falls. Just plug in the two percentages with their correct signs — positive for an increase, negative for a decrease — and read off the net change. If the net comes out positive there is an overall gain; if negative, an overall fall. Memorising the single equivalent factor for the discounts you meet often (20% and 10% gives 28%; two 10% discounts give 19%) will let you answer many marked-price questions without writing a single intermediate step.
The ratio method for fast CP-SP problems
Many AFCAT problems hide the actual money values and only give percentages. Treating CP and SP as a clean ratio lets you skip the rupee figures entirely.
At profit% p, CP : SP = 100 : (100 + p). At loss% L, CP : SP = 100 : (100 − L). Plug the ratio straight into the data and solve.
By selling an article for ₹360 a man gains as much as he would lose by selling it for ₹240. Find the cost price.
When the gain and the loss are equal in rupees, the CP is simply the average of the two selling prices — here (360 + 240) ÷ 2 = 300. Spotting that pattern turns a two-line algebra problem into a one-line mental sum.
Dishonest dealer and false-weight problems
A favourite AFCAT trap: a shopkeeper sells at cost price but cheats on the weight, using (say) a 900 g weight in place of 1 kg. His real profit comes from the short weight.
Gain% = (Error ÷ (True value − Error)) × 100
where Error = true weight − weight actually given.
A dealer professes to sell at cost price but uses a 900 g weight for 1 kg. Find his gain percent.
The denominator is the weight he actually gives (900 g), not the 1000 g he claims. The error is profit measured against what the customer really receives.
These dishonest-dealer items look intimidating but always reduce to the same idea: the seller spends money on the short weight he hands over and charges for the full claimed weight, so his cost is tied to the smaller quantity. Whenever a question says “sells at cost price but uses a faulty weight” or “gains by under-measuring,” reach straight for the error-over-given formula rather than building rupee values. If the dealer additionally marks the goods up by a percentage, find the weight gain first and then combine it with that markup using the successive-percentage rule from the previous section.
The equal-price two-article trap
When two articles are sold at the same selling price, one at x% profit and the other at x% loss, the dealer always ends up with a net loss — never break-even.
Net loss% = (Common%)2 ÷ 100 = (x ÷ 10)2.
Two watches are sold at the same price; one at 20% profit, the other at 20% loss. Find the overall loss percent.
Students answer “no profit no loss” because +20% and −20% seem to cancel. They do not — equal SP with equal % always yields a loss of (x÷10)% squared.
Cost of one set equals selling price of another
Another high-frequency type: “the CP of 20 articles equals the SP of 16 articles — find the profit percent.” Treat the article count as the price ratio.
If CP of a articles = SP of b articles, then Profit/Loss% = ((a − b) ÷ b) × 100. A positive answer is profit, a negative one is loss.
The cost price of 20 articles equals the selling price of 16 articles. Find the gain percent.
Because fewer articles were sold to recover the cost of more, the seller has gained. The formula works directly from the two counts — no need to assume any rupee value.
Previous-year style question
Q. A shopkeeper marks his goods 40% above the cost price and then allows a discount of 25% on the marked price. Find his net profit or loss percent.
Answer: Let CP = ₹100. Marked Price = 100 + 40% = ₹140. Discount of 25% on 140 = 140 × 0.75 = ₹105 = Selling Price. Profit = 105 − 100 = ₹5, so Profit% = 5%. The shopkeeper makes a net profit of 5%.
Traps and time-savers to keep in mind
- Calculating profit% on the selling price instead of the cost price.
- Adding two successive discounts directly instead of using a + b + ab÷100.
- Using 1000 g instead of the 900 g actually given in false-weight sums.
- Assuming equal % profit and loss on equal SP cancel out — they cause a loss.
Always assume CP = ₹100 when the question gives only percentages. Every figure then turns into an easy percentage, and the final profit% reads off directly. This one habit speeds up the majority of marked-price problems.
Quick revision
- Profit = SP − CP; Loss = CP − SP; both percents are on CP.
- SP = CP × (100 ± %)÷100; reverse to find CP by dividing.
- Discount is on MP: SP = MP × (100 − D%)÷100.
- Successive changes: net% = a + b + ab÷100.
- False weight gain% = Error ÷ (true − error) × 100.
- Equal SP, equal % profit and loss → loss of (x÷10)2 %.
- Assume CP = ₹100 whenever only percentages are given.
Frequently asked questions
Are profit and loss percent always taken on the cost price?
Yes, unless the question explicitly states otherwise. Profit% and loss% are calculated on the cost price, while discount% is calculated on the marked price. Keeping these two bases separate prevents most errors.
Can two successive discounts of 20% and 10% be added to 30%?
No. The second discount applies to the already-reduced price. The correct equivalent is 20 + 10 minus (20 times 10)/100 = 28%, so a single discount of 28%, not 30%.
Why does selling two items at the same price with equal profit and loss percent cause a loss?
Because the percentages act on different cost prices. The net result is always a loss equal to (common percent divided by 10) squared, for example 4% when the common percent is 20.
How do I find the cost price quickly when only the selling price and profit percent are given?
Divide the selling price by the multiplying factor. For a 15% profit, CP = SP divided by 1.15. Never just take 15% of the SP and subtract, as that uses the wrong base.
What is the fastest approach when a question gives only percentages?
Assume the cost price is 100 rupees. Every marked price, discount and selling price then becomes a simple percentage of 100, and the final profit or loss percent can be read off directly.
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