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CDS Mathematics · Percentage, Profit and Loss

Discounts and Marked Price

A discount is a percentage of the marked price; successive discounts multiply, and profit is still measured on the cost.

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Why this matters

Seven PYQs, one of them HARD. Four chain three successive discounts, which multiply exactly like successive changes; the other three link marked price, discount and profit, where the marked price and the cost price are two different bases.

Concept 1 of 1: Marked price, discount and profit

The shop marks a price, takes a discount off the MARKED price, and the customer pays what is left. Whether that makes a profit is judged against the COST, a different number.

Definition

  • SP=MP(1−d100)\text{SP} = \text{MP}\left(1 - \dfrac{d}{100}\right).
  • Successive discounts d1,d2,d3d_1, d_2, d_3: the customer pays (1−d1100)(1−d2100)(1−d3100)\left(1 - \tfrac{d_1}{100}\right)\left(1 - \tfrac{d_2}{100}\right)\left(1 - \tfrac{d_3}{100}\right) of MP; the single equivalent discount is 11 minus that.
  • Mark up m%m\% over cost, then discount d%d\%: SP =CP(1+m100)(1−d100)= \text{CP}\left(1 + \tfrac{m}{100}\right)\left(1 - \tfrac{d}{100}\right).
  • Bought at a discount: the price paid is (100−d)%(100 - d)\% of the listed price.

Successive discounts

1−(1−d1100)(1−d2100)1 - \left(1 - \tfrac{d_1}{100}\right)\left(1 - \tfrac{d_2}{100}\right)

Worked example

Find the single discount equal to successive discounts of 25%25\% and 20%20\%.
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (I) 2021 — Elementary Mathematics · Q31Moderate

Example 1 · Percentage, Profit and Loss · Successive Discount and Marked Price

A trader gives successive discounts of 20%, 10% and 5% respectively. What is the overall discount?

Discounts do not add

Discounts of 20%20\%, 10%10\% and 5%5\% come to 31.6%31.6\%, not 35%35\%. Each is taken off the price left by the one before.

Two bases in one question

The discount is a percentage of the MARKED price; the profit is a percentage of the COST. Keep them apart: CP 100100, MP 120120, 10%10\% off gives SP 108108, an 8%8\% profit.
Drill 6 more on marked price, discount and profit

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

  • Marked price, discount and profit

    Successive discounts

    1−(1−d1100)(1−d2100)1 - \left(1 - \tfrac{d_1}{100}\right)\left(1 - \tfrac{d_2}{100}\right)

Watch out for (2)

Test yourself on Percentage, Profit and Loss

15 past CDS questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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