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Rajiv sold an article for Rs.56 which cost him Rs.x. If he had gained x% on his outlay, what was his cost?

Question

Rajiv sold an article for Rs.56 which cost him Rs.x. If he had gained x% on his outlay, what was his cost?

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Solution

To solve this problem, we need to set up an equation based on the information given in the question.

  1. We know that Rajiv sold an article for Rs.56 and he gained x% on his outlay (cost).

  2. The selling price (SP) of an article is calculated as follows: SP = Cost Price (CP) + Gain.

  3. The gain is calculated as a percentage of the cost price, so Gain = (x/100)*CP.

  4. Substituting the gain in the selling price formula, we get SP = CP + (x/100)*CP.

  5. Simplifying this, we get SP = CP(1 + x/100).

  6. We know that the selling price is Rs.56, so we can substitute this into the equation to get 56 = CP(1 + x/100).

  7. We also know from the question that the gain was x%, which means that x/100 = Gain/CP.

  8. Substituting this into the equation, we get 56 = CP(1 + Gain/CP).

  9. Simplifying this, we get 56 = CP + Gain.

  10. But we know that Gain = x, so 56 = CP + x.

  11. Rearranging this equation to solve for CP, we get CP = 56 - x.

So, the cost of the article was Rs.(56 - x).

This problem has been solved

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