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Profit, Loss & Discount for CAT: Formulas, Weightage & Question Types

CP, marked price and SP as multipliers, and the same-price trap.

Profit, Loss & Discount formula sheet

Everything CAT needs from Profit, Loss & Discount, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. CP is cost price, MP the marked or list price, SP the selling price.

The definitions, and what each percentage is of

ProfitSP−CP\text{SP} - \text{CP}
Profit %SP−CPCP×100\dfrac{\text{SP}-\text{CP}}{\text{CP}} \times 100 — always on CP
Discount %MP−SPMP×100\dfrac{\text{MP}-\text{SP}}{\text{MP}} \times 100 — always on MP
Selling at p%p\% profitSP=CP(1+p100)\text{SP} = \text{CP}\left(1+\dfrac{p}{100}\right)
Selling at l%l\% lossSP=CP(1−l100)\text{SP} = \text{CP}\left(1-\dfrac{l}{100}\right)
After a discount d%d\%SP=MP(1−d100)\text{SP} = \text{MP}\left(1-\dfrac{d}{100}\right)

The chain — this is the chapter

Linking all threeMP(1−d100)=CP(1+p100)\text{MP}\left(1-\dfrac{d}{100}\right) = \text{CP}\left(1+\dfrac{p}{100}\right)
So the markup over costMPCP=1+p1001−d100\dfrac{\text{MP}}{\text{CP}} = \dfrac{1+\frac{p}{100}}{1-\frac{d}{100}}
Successive discountsmultiply: (1−d1)(1−d2)(1-d_1)(1-d_2), they never add

Two useful consequences

Two items at the same SP, one at +x%+x\% and one at −x%-x\%always a net loss of x2100%\dfrac{x^2}{100}\%
Equal numbers at +x%+x\% and −x%-x\% on the same CPexactly break even

False weights and free goods

Gives ff while charging for ttprofit %=t−ff×100\% = \dfrac{t-f}{f}\times 100
Gets gg free per tt boughtthe effective cost per unit is paidt+g\dfrac{\text{paid}}{t+g}
Both at oncework in cost per unit and revenue per unit, then compare

Several lots

Overall profit %total SP−total CPtotal CP×100\dfrac{\text{total SP} - \text{total CP}}{\text{total CP}} \times 100
Neverthe average of the individual profit percentages
Cost of a mixturethe weighted average of the component costs

The 6 Profit, Loss & Discount question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

  1. 01

    Part at one margin, part at another

  2. 02

    Mark it up, then discount it

  3. 03

    Goods of different kinds, mixed and sold together

  4. 04

    A chain of resales

  5. 05

    Two scenarios, two equations

  6. 06

    Same price, or a crooked measure

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Profit, Loss & Discount in CAT: quick answers

How many Profit, Loss & Discount questions come in CAT Quant?
About 0.9 questions in a 22-question Quant section, worth roughly 3 marks. Profit, Loss & Discount appeared in 19 of the 24 CAT papers from 2017 to 2025, 25 questions in all, which ranks it 13 of 25 Quant chapters.
Are Profit, Loss & Discount questions in CAT MCQ or TITA?
24% of the Profit, Loss & Discount questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Profit, Loss & Discount questions does CAT ask?
CAT keeps returning to 6 question shapes in Profit, Loss & Discount: Part at one margin, part at another; Mark it up, then discount it; Goods of different kinds, mixed and sold together; A chain of resales; Two scenarios, two equations; Same price, or a crooked measure.

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