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IntermediateMedium-HardMCQ Source: LaTeX
Arithmetic/Profit & Loss

Question

[Arithmetic -- Profit & Loss, Medium-Hard, MCQ]

A retailer marks every item in his store at 60% above its cost price. As part of a promotion, on every third item that is sold he gives a discount of dd% on the marked price, while the remaining items are sold at the marked price. Over a block of 9 items sold under this scheme, his overall profit is exactly 40%. The value of dd is:

Options

A

30

B

32.5

C

35

D

37.5

Answer

(D) 37.5.

Detailed solution

[Profit on a block of items]

Let cost price of each item be 100100 units. Marked price =160= 160.

  • Out of every 9 items: 6 are sold at MP =160= 160 and 3 are sold at 160(1−d/100)160(1 - d/100).
  • Total cost over 9 items =900= 900.
  • Total revenue =6(160)+3⋅160 ⁣(1−d100)=960+480 ⁣(1−d100)= 6(160) + 3 \cdot 160\!\left(1 - \tfrac{d}{100}\right) = 960 + 480\!\left(1 - \tfrac{d}{100}\right).

Overall profit =40= 40% \Rightarrow revenue =1260= 1260.

$

960 + 480 - 4.8 d = 1260 ;\Longrightarrow; 4.8 d = 180 ;\Longrightarrow; d = 37.5.

$

Answer: (D) 37.5.

Why CAT-level: Tempting first move is to apply a simple discount-on-MP formula on a single item; the trap is the weighted base of 9 items.

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