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Select the correct answerAnu sold an article for Rs.480 at some profit. Had she sold it for Rs.400, then there would have been a loss equal to one-third of the initial profit. What was the cost price of the article?OptionsRs.450Rs.430Rs.420Rs.425

Question

Select the correct answerAnu sold an article for Rs.480 at some profit. Had she sold it for Rs.400, then there would have been a loss equal to one-third of the initial profit. What was the cost price of the article?OptionsRs.450Rs.430Rs.420Rs.425

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Solution

To solve this problem, we need to set up a couple of equations based on the information given.

Let's denote:

  • C as the cost price of the article
  • P as the initial profit when the article was sold for Rs.480

From the problem, we know that:

  1. C + P = 480 (since the cost price plus the profit equals the selling price)

  2. C - 400 = P/3 (since when the article was sold for Rs.400, the loss was one-third of the initial profit, which means the cost price minus Rs.400 equals one-third of the profit)

Now we can solve these equations step by step.

First, express P from the first equation:

P = 480 - C

Then substitute P in the second equation:

C - 400 = (480 - C) / 3

Multiply all terms by 3 to get rid of the fraction:

3C - 1200 = 480 - C

Add C to both sides:

4C - 1200 = 480

Add 1200 to both sides:

4C = 1680

Finally, divide both sides by 4 to solve for C:

C = 1680 / 4 = Rs.420

So, the cost price of the article was Rs.420.

This problem has been solved

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