Reena makes a profit of 20% by selling pens at a certain price. If she charges ₹5 more on each pen, she will gain 40%. The initial selling price of one pen was:

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Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 26 Jun, 2024 Shift 1)

Answer 1

Given:

Profit Percentage 1 = 20%

Profit Percentage 2 = 40%

Increase in Selling Price = ₹5

Formula Used:

Selling Price (SP) = Cost Price (CP) + Profit

Profit = (Profit Percentage × CP) / 100

Calculation:

Let the initial Cost Price (CP) be ₹x.

Initial Selling Price (SP₁) = CP + Profit

Profit for SP₁ = (20% of CP) = (20/100) × x

SP₁ = x + (20/100) × x

SP₁ = x + 0.2x

SP₁ = 1.2x

New Selling Price (SP₂) = SP₁ + ₹5

SP₂ = 1.2x + 5

Profit for SP₂ = (40% of CP) = (40/100) × x

SP₂ = x + (40/100) × x

SP₂ = x + 0.4x

SP₂ = 1.4x

Given SP₂ = 1.2x + 5

⇒ 1.4x = 1.2x + 5

⇒ 1.4x - 1.2x = 5

⇒ 0.2x = 5

⇒ x = 5 / 0.2

⇒ x = 25

Initial Selling Price (SP₁) = 1.2x

SP₁ = 1.2 × 25

SP₁ = 30

The initial selling price of one pen was ₹30.

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