CAT Profit Loss Discount Formula Sheet PDF 2026

Q: Is discount always calculated on cost price?

No. Discount is always calculated on marked price, while profit and loss are always calculated on cost price. Mixing the two bases is the single most common error in this topic.

Q: Do two successive discounts of 20% and 10% add up to 30% off?

No. The discounts multiply as factors: 0.8 times 0.9 gives 0.72, an effective 28% off. Successive discounts always give a smaller total than adding the two percentages.

Q: If I sell two items at the same price, one at a 10% profit and one at a 10% loss, do I break even?

No. The result is always a small loss, equal to (x/10) squared percent. At 10%, that works out to a 1% loss overall, purely because the two items had different cost prices even though they sold for the same amount.

Q: How common is the false weight trick in CAT?

It appears regularly inside profit and loss sets, usually disguised as a shop selling at cost price while using a lighter weight. The profit comes entirely from the weight gap.

Q: Can the PDF be downloaded for free?

Yes. All 6 pages can be read on this page or downloaded at no cost, so it can be printed or kept on a phone for last-minute revision.

CAT Profit, Loss and Discount formula sheet, free to download as a 6-page PDF. The topic carries about 9 to 12 marks across roughly 4 questions a year, and takes roughly ten minutes to work through, so it earns a slot before the exam.

Built for revision, so every line trades explanation for speed. Read the working behind each formula in the full Profit, Loss and Discount notes before leaning on this sheet.

Two Bases, Never Swapped

Profit% = (SP−CP)/CP × 100, and Loss% = (CP−SP)/CP × 100. Both sit on Cost Price, never on SP.

Discount% is read the same way off Marked Price: SP = MP × (100−d)/100, and MP = SP × 100/(100−d). A profit of 25% does not put CP at 75% of SP; CP = SP × 100/125.

Repair, freight or installation costs paid before resale count toward CP too, added before the profit percentage is worked out. A cycle bought for Rs.4500 with Rs.500 spent on repair has an effective CP of Rs.5000, so a sale at Rs.5750 is a 15% profit, not 750/4500.

Two Articles, One Selling Price

Sell two articles at the same SP, one at x% profit and the other at x% loss on its own CP, and the outcome is always a loss: overall loss% = (x/10)². A pair sold this way at x = 10 loses 1% overall; at x = 20 it loses 4%.

The result never depends on what the actual SP was, and it is never break-even, even though the two percentages look like they should cancel.

Chaining Discounts Without Adding Them

For discounts p%, q%, r% in sequence: SP = MP × (100−p)(100−q)(100−r) / 100³. 20% then 10% off multiplies to 0.8 × 0.9 = 0.72, an effective 28% off, not 30%. Order never changes the total, since multiplication commutes.

Markup then discount: net% = x − d − xd/100, where MP is x% above CP and d% is the discount. A markup of 40% followed by a 25% discount nets 40 − 25 − 10 = 5% profit, not the 15% a quick subtraction would suggest.

Running that formula backwards gives the marked price needed for a target profit: MP = CP × (100+p)/(100−d). For a target profit of 20% after a 10% discount on CP 500, MP = 500 × 120/90 = 666.67, which checks out at 666.67 × 0.9 = 600 = 500 × 1.2.

Batch Pricing Without a CP or SP Value

CP of x articles = SP of y articles ⇒ Profit% = (x−y)/y × 100 when x > y, or Loss% = (y−x)/y × 100 when x < y.

CP of 20 articles = SP of 16: profit = (20−16)/16 × 100 = 25%. Spot this setup from wording like "cost price of n articles equals the selling price of m articles."

The False Weight Trick

A shop can advertise no markup at all and still profit, by handing over less than the stated weight.

Profit% = (W−w)/w × 100, where W is the true weight and w the false weight actually given. Claiming 1000g but delivering 800g gives a 25% profit at the same sticker price, with no stated markup at all.

Combined with a stated profit% on top: overall profit% = [(W/w) × (100+stated%)/100 − 1] × 100. The weight gain and the stated margin both act as multipliers on cost price, so combine them before subtracting 1, never by adding the two percentages.

Profit, Loss and Discount Worked Through on Video

Source: MBA Wallah

How to Revise From It

The closing page repeats every formula in one table, each checked against a cost price of 100.

Cover the formula column and reproduce it from the quantity name
Fix which base each line uses before writing anything down
Re-derive the markup-then-discount formula rather than memorising the final expression alone
Check for a false-weight trick whenever a question mentions weights or measures

CAT Profit Loss Discount Formula Sheet FAQs

Ques. Is discount always calculated on cost price?

Ans. No. Discount is always calculated on marked price, while profit and loss are always calculated on cost price. Mixing the two bases is the single most common error in this topic.

Ques. Do two successive discounts of 20% and 10% add up to 30% off?

Ans. No. The discounts multiply as factors: 0.8 times 0.9 gives 0.72, an effective 28% off. Successive discounts always give a smaller total than adding the two percentages.

Ques. If I sell two items at the same price, one at a 10% profit and one at a 10% loss, do I break even?

Ans. No. The result is always a small loss, equal to (x/10) squared percent. At 10%, that works out to a 1% loss overall, purely because the two items had different cost prices even though they sold for the same amount.

Ques. How common is the false weight trick in CAT?

Ans. It appears regularly inside profit and loss sets, usually disguised as a shop selling at cost price while using a lighter weight. The profit comes entirely from the weight gap.

Ques. Can the PDF be downloaded for free?

Ans. Yes. All 6 pages can be read on this page or downloaded at no cost, so it can be printed or kept on a phone for last-minute revision.