The pie chart below shows the percentage break-up of the costs incurred in printing a magazine. For a given issue of the magazine, 2% of the total cost equals Rs. 2,000, and the print run is 12,500 copies. What should the sale price of each copy be if the publisher wants a profit of 5%?
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Find the total cost from the 2% figure, add 5% profit, then divide by the number of copies.
Instead of adding the profit to the total cost first, work out the cost of a single copy first and then add the profit margin to that one number.
Rs. 5: at this price, total sales would be $5 \times 12500 = Rs. 62,500$, far below the required cost of Rs. 1,00,000 itself, so this cannot be right.
Rs. 7.5: total sales here would be $7.5 \times 12500 = Rs. 93,750$, which is still less than the Rs. 1,00,000 cost, meaning a loss, not a 5% profit, so this is wrong.
Rs. 8: the cost per copy alone is $\dfrac{1,00,000}{12,500} = Rs. 8$, so selling at exactly Rs. 8 covers only the cost, with zero profit, ruling this option out.
Rs. 8.40: adding a 5% margin to the Rs. 8 per copy cost gives $8 \times 1.05 = Rs. 8.40$, which matches the required 5% profit exactly.
Working per copy first, the cost is Rs. 8, and the 5% profit takes it to Rs. 8.40.
Let's summarize:
First find the cost per copy by dividing total cost by the print run.
Add the 5% profit margin to that per copy cost, not to the total separately.
The two approaches, total first or per copy first, must agree, and both give Rs. 8.40.
So the sale price of each copy should be Rs. 8.40.
