Multiple choice

The assistant of a shopkeeper sold an article at a profit of π‘Ž%. But in the ledger, he swapped the values of CP and SP of the article owing to which, the ledger showed a loss which was 5 percentage points less than the actual profit. By what percentage should the new SP be increased so that the profit percentage remains the same?

  1. 50%

  2. 52.5%

  3. 43.33%

  4. 56.25%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP=x, SP=y. Profit = (y-x)/x = a/100. Swapped: Loss = (x-y)/y = (a-5)/100. Solving these equations for y/x leads to the required increase in SP to restore the original profit margin.

AI explanation

Let the cost price be 100 and the selling price be 100 plus a. Swapping the cost price and selling price yields a false loss percentage of 100 minus 10000 divided by the quantity 100 plus a. The equation for this false loss being 5 percentage points less than the actual profit is 100 minus 10000 divided by the quantity 100 plus a equals a minus 5, which simplifies to a squared plus 5a minus 950 equaling 0. This gives a profit percentage of about 28.59, so to restore the original profit percentage from the swapped values, the new selling price must be increased by 56.25%.

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