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 $R S 30.09$ for it, find the cost of the manufacturer.

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Solution

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

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