Question

The maximum retail price(MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage for the manufacturer who sells his product to the retailer? The retailer gives a 10% discount on the MRP.

Answer 1

Hint: This problem requires the concept profit, loss and percentages. We will first assume the manufacturing cost to be Rs 100, because this will make the calculations in percentages easier. We will then find the MRP by adding 55 to the manufacturing cost. We will then assume the selling price of the manufacturer as x, which can be computed using the conditions given.

Complete step-by-step answer:
We will first try to visualize all the steps involved here. The manufacturer makes a product, and sells it to a retailer at some profit, which we need to find. The retailer further sells the product at a 23% profit with a 10% discount at MRP. The net profit between the manufacturing cost and MRP is 55%.
We will begin by assuming the manufacturing cost to be Rs. 100. This is because we can directly add or subtract the percentages without converting them into a decimal form. So,
M = Rs. 100
It is given that the MRP is 55% above the manufacturing cost so-
MRP = M + 55 = 100 + 55 = Rs. 155
Let the selling price of the manufacturer be Rs. x. We have been given that the selling price by the retailer has a discount of 10%, which can be calculated as-
$SP = 155 - 10\% \;of\;155 = 155 - \dfrac{{10}}{{100}} \times 155 = 155 - 15.5 = Rs.\;139.5$
Also, it has been given that the profit earned by the retailer is 23% on the SP. This means that-
$\begin{align}
  &SP = x + 23\% \;of\;x \\
  &139.5 = x + \dfrac{{23\;}}{{100}}x \\
  &139.5 = \dfrac{{x\left( {100 + 23} \right)}}{{100}} = \dfrac{{123x}}{{100}} \\
  &x = 139.5 \times \dfrac{{100}}{{123}} = Rs.\;113.41 \\
\end{align} $
We need to find the profit earned by the manufacturer. Since we assumed the manufacturing cost as Rs. 100, we can directly subtract the selling price(x) and the manufacturing cost(M). So the percent profit is-
x - M = 113.41 - 100 = 13.41%
This is the answer.

Note: In such types of questions, we should always try to find the different cost and selling prices in terms of 100, because it makes calculation much easier. A common mistake here is that students directly subtract Rs 10 while calculating the discounted price on the MRP. This is wrong because the discount of 10% is not on Rs. 100, but on Rs. 155, so we cannot directly add or subtract the discount in this case.