If the selling price of a bed is 2-times of initial, then the profit is 10-times of initial. Find the initial profit percentage (in %).

400

12.5

500

APEDIA

NTPC Graduate Tier 1

2025 • 05 Jun, 2025 • Shift-3

If the selling price of a bed is 2-times of initial, then the profit is 10-times of initial. Find the initial profit percentage (in %).

Correct Answer

12.5

[Variable Initialization]: Let the Cost Price be represented as 'C' and the original Selling Price be 'S'. The initial profit generated is mathematically P1 = S......

💡 Analysis & Explanation

[Variable Initialization] ▼

Let the Cost Price be represented as 'C' and the original Selling Price be 'S'. The initial profit generated is mathematically P1 = S - C.

[Scenario Projection] ▼

If the selling price is doubled, the new selling price becomes '2S'. The newly calculated profit is P2 = 2S - C.

[Constraint Application] ▼

The problem states that this new profit is ten times the original profit. Thus, 2S - C = 10 × (S - C).

[Algebraic Simplification] ▼

Expanding the equation yields 2S - C = 10S - 10C. Rearranging terms gives 9C = 8S, which means S = (9/8)C.

[Percentage Derivation] ▼

The initial profit P1 is S - C = (9/8)C - C = C/8. To find the percentage, divide the profit by the cost price and multiply by 100: (C/8) / C × 100 = 100 / 8 = 12.5%.

Conclusion ▼

The baseline profit percentage stands at 12.5%.

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If the selling price of a bed is 2-times of initial, then the profit is 10-times of initial. Find the initial profit percentage (in %).