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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 $$20\%$$. 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.


Solution

Manufactures $$18\%$$ Wholesaler $$20\%$$ Retails $$25\%$$ bCustomer
Let cost price of manufacture be $$Rs. x$$
$$\therefore $$ profit $$=Rs. \dfrac {18x}{100}$$
$$\therefore $$ Selling price of manufacture $$=Rs.\ \dfrac {118x}{100}=$$ Cost price of Wholesaler
Profit $$=Rs.\ \left (\dfrac {26}{100} \times \dfrac {118s}{100} \right)=Rs.\ \dfrac {236x}{1000}$$
$$\therefore \ $$ Selling price of wholesaler $$=Rs.\ \left (\dfrac {118x}{100} \times \dfrac {236x}{1000} \right)=Rs.\ \dfrac {1416x}{1000}$$
$$=Cost price of retails
Profit $$Rs.\ \left (\dfrac {25}{100} \times \dfrac {1416x}{1000} \right) =Rs.\ \dfrac {354x}{1000}$$
$$\therefore \ $$ Selling price of retails $$=Rs.\ \left (\dfrac {1416x}{1000} +\dfrac {354x}{1000} \right)$$
$$=Rs.\ \dfrac {1770x}{1000}=Rs.\ \dfrac {177x}{100}$$
=Cost price of customer
$$\therefore \ \dfrac {177x}{100}=\dfrac {3009}{100}$$
or, $$\boxed {x=17}$$
Ans: Cost price of manufacture is $$Rs. 17$$

Mathematics

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