A man sells an article at a profit of 25%. If the had bought it at 20% less…

2024

A man sells an article at a profit of 25%. If the had bought it at 20% less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost price of the article.

  1. A.

    Rs. 20

  2. B.

    Rs. 30

  3. C.

    Rs. 40

  4. D.

    Rs. 50

Attempted by 1 students.

Show answer & explanation

Correct answer: D

Step-by-Step Solution

To find the cost price, we can set up an algebraic equation based on the two scenarios described.

  1. Define the variables:

    • Let the original Cost Price (CP) be C.

    • Original Profit = 25%.

    • Therefore, the original Selling Price (SP) = C + 0.25C = 1.25C.

  2. Define the second scenario:

    • New Cost Price (CP') = C - 20% of C = 0.8C.

    • New Selling Price (SP') = SP - 10.50 = 1.25C - 10.50.

    • New Profit = 30%.

    • Therefore, SP' = CP' + 30% of CP' = 1.3 * CP'.

  3. Solve the equation:

    • Substitute the expressions into the second scenario equation: 1.25C - 10.50 = 1.3 * (0.8C)

    • 1.25C - 10.50 = 1.04C

    • 1.25C - 1.04C = 10.50

    • 0.21C = 10.50

    • C = 10.50 / 0.21

    • C = 50.

The original cost price of the article is Rs. 50.

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