Question

Manufacturer sells an article to a wholesaler at a profit of 18%. The wholesaler sells it to a retailer at a profit at 20%. The retailer sells to a customer at a profit of 25%. If the customer pays Rs.30.09 for it, find the cost of the manufacturer.

Answer 1

Hint: In this question, an article is sold from a manufacturer to a wholesaler then from the wholesaler to a retailer, then from a retailer to the customer. Every seller makes a profit and we have to find the cost of the article for the manufacturer if the cost for the customer is given. For this we will use the formula: $SP=CP\left( \dfrac{100+\text{Profit}\%}{100} \right)$ where SP is the selling price, CP is the cost price.

Complete step-by-step answer:
Let us suppose that, the cost price for the article for the manufacturer is Rs.x
Now the manufacturer sold the article at profit of 18% to the wholesaler.
We know, $SP=CP\left( \dfrac{100+\text{Profit}\%}{100} \right)$ where SP is the selling price and CP is the cost price. So, selling price for manufacturer becomes equal to,
\[\begin{align}
  & \Rightarrow SP=x\left( \dfrac{100+18}{100} \right) \\
 & \Rightarrow SP=\dfrac{118}{100}x \\
 & \Rightarrow SP=\dfrac{59}{50}x \\
\end{align}\]
Hence the selling price for the manufacturer is $Rs.\dfrac{59}{50}x$ which becomes the cost price for the wholesaler. So,
CP for wholesaler is $Rs.\dfrac{59}{50}x$.
Now, wholesaler sold it to retailer at a profit of 20% so,
\[\begin{align}
  & SP=CP\left( \dfrac{100+\text{Profit}\%}{100} \right) \\
 & \Rightarrow \dfrac{59}{50}x\left( \dfrac{100+20}{100} \right) \\
 & \Rightarrow \dfrac{59}{50}x\times \dfrac{120}{100} \\
 & \Rightarrow Rs.\dfrac{354}{250}x=Rs.\dfrac{177}{125}x \\
\end{align}\]
Hence the selling price for wholesalers is $Rs.\dfrac{177}{125}x$ which becomes the cost price for the retailer. So,
CP for the retailer is $Rs.\dfrac{177}{125}x$.
The retailer sold the article to the customer at a profit of 25% so,
\[\begin{align}
  & SP=CP\left( \dfrac{100+\text{Profit}\%}{100} \right) \\
 & \Rightarrow \dfrac{177}{125}x\left( \dfrac{100+25}{100} \right) \\
 & \Rightarrow \dfrac{177}{125}x\times \dfrac{125}{100} \\
 & \Rightarrow Rs.\dfrac{177}{100}x \\
\end{align}\]
So the selling price for the retailer becomes $Rs.\dfrac{177}{100}x$ which becomes the cost price for the customer.
Hence, the cost price for the customer becomes $Rs.\dfrac{177}{100}x$.
We are given the cost price for customer as Rs.30.09 so, both the value will be equal, we get:
$Rs.\dfrac{177}{100}x=30.09$.
Writing 30.09 as $\dfrac{3009}{100}$ we get
$\dfrac{177}{100}x=\dfrac{3009}{100}$.
Cancelling 100 from both sides of the equation, we get
$177x=3009$.
Dividing both sides by 177, we get
$x=\dfrac{3009}{177}=17$.
Hence the value of x is 17.
Since x was supposed to be the cost price for the manufacturer. So our required answer is Rs.17

Note: Students should take care of the signs while solving the equation. Students should do all the calculations carefully as large numbers are involved. Take care while applying the formula. In place of P%, we have to put a magnitude of percentage and need not divide by 100 again as 100 is already divided in the formula.