Question

A manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18%. The wholesaler sells the same to a retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs.30.09, thereby earning a profit of 25%. The cost price for the manufacturer?
A. $Rs.15$
B. $Rs.16$
C. $Rs.17$
D. $Rs.18$

Answer 1

Hint: The concept of successive profit will be applied in this question. Let the cost price for the manufacturer be $p$. For Wholesale dealers, it will become $p + 18\% p$. For retailers it will become $p + 18\% p + 20\% (p + 18\% p)$. Further, it is given that the profit earned by the retailer is 25% when the selling price is Rs.30.09. We will apply the formula of profit i.e., $p\% = \dfrac{{S.P - C.P}}{{C.P}} \times 100$, where S.P is selling price and C.P is cost price.

Complete step-by-step answer:
Let the cost price for manufacturer be $p$
As, mentioned in question the manufacture sells it at a profit of 18%
Therefore, the cost price for whole seller is $p + 18\% p$
 $ = p + \dfrac{{18}}{{100}}p = \dfrac{{118}}{{100}}p$
Now, the wholesaler sells it at a profit of 20%.
Therefore, the cost price for Retailer is $p + 18\% p + 20\% (p + 18\% p)$
$
   = \dfrac{{118}}{{100}}p + \dfrac{{20}}{{100}} \times \dfrac{{118}}{{100}}p \\
   = \dfrac{{345}}{{250}}p \\
$
Now, the retailer sells it at a profit of 25%.
Therefore, the selling price for retailer is
$
  \dfrac{{345}}{{250}}p + \dfrac{{25}}{{100}} \times \dfrac{{345}}{{250}}p \\
   = \dfrac{{805}}{{500}}p \\
$
The selling price given in the question is Rs.30.09
$
   \Rightarrow \dfrac{{805}}{{500}}p = 30.09 \\
   \Rightarrow p = 17 \\
 $
 Hence, The Cost Price for the manufacturer is Rs.17

So, the correct answer is “Option C”.

Note: Important aspect to notice and keep in mind is that the cost price for the one becomes the selling price for the other. As in this question, the selling price of the manufacturer becomes the cost price of the wholesaler. Further, the selling price of the whole seller becomes the cost price of the retailer. The shortcut way to do this problem and finding the cost price, say P is
$p = \dfrac{{100}}{{100 + {p_1}}} \times \dfrac{{100}}{{100 + {p_2}}} \times \dfrac{{100}}{{100 + {p_3}}} \times s.p$, where ${p_1},{p_2}$ and ${p_3}$ are the profits given and $s.p$ is the selling price. Putting ${p_1} = 18,{p_2} = 20$,${P_3} = 25$ and $s.p = 30.09$.
$
   \Rightarrow P = \dfrac{{100}}{{118}} \times \dfrac{{100}}{{120}} \times \dfrac{{100}}{{125}} \times 30.09 \\
   \Rightarrow P = 17 \\
$