Question

A manufacturer sells an article to a wholesaler at a profit of 18%, the wholesaler sells it to a retailer at a profit of 20%, and the retailer sells it 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: To find the cost of manufacturer we carefully form relations between manufacturer, wholesaler, retailer and customer as per the given data. Also, profit = selling price – cost price and profit = profit percent × cost price.

Complete step-by-step answer:

Given Data,
Manufacturer 18%, Wholesaler 20%, Retailer 25%, and Customer pays 30.09.
Let the cost price of manufacturer be Rs.x
⟹profit = Rs\[\dfrac{{{\text{18x}}}}{{100}}\]
∴Selling price of manufacturer = Rs\[\dfrac{{{\text{118x}}}}{{100}}\]= Cost price of wholesaler
Profit = Rs $\left( {\dfrac{{20}}{{100}} \times \dfrac{{118{\text{x}}}}{{100}}} \right) = {\text{Rs}}\dfrac{{236{\text{x}}}}{{1000}}$
∴Selling price of wholesaler = Rs $\left( {\dfrac{{236{\text{x}}}}{{1000}} + \dfrac{{118{\text{x}}}}{{100}}} \right) = {\text{Rs}}\dfrac{{{\text{1416x}}}}{{1000}}$= Cost price of retailer
⟹Profit = Rs $\left( {\dfrac{{1416{\text{x}}}}{{1000}} \times \dfrac{{25}}{{100}}} \right) = {\text{Rs}}\dfrac{{{\text{354x}}}}{{1000}}$
∴Selling price of retailer = Rs $\left( {\dfrac{{1416{\text{x}}}}{{1000}} + \dfrac{{354{\text{x}}}}{{100}}} \right) = {\text{Rs}}\dfrac{{{\text{1770x}}}}{{1000}} = {\text{Rs}}\dfrac{{177{\text{x}}}}{{100}}$
⟹Cost price of customer
⟹$\dfrac{{177{\text{x}}}}{{100}} = 30.09$
⟹x = 17.
Cost price of the manufacturer is Rs.17.

Note: In order to solve this type of question the key concept is to make relations between given terms with respect to the data given. After carefully establishing relations we use the formulae of cost price and profit to compute the answer.