Question

A wholeseller sold an article to the retailer at a profit of 10%. The retailer then sold the
article to the customer for $264 at a profit of 20%. Find the cost price of the article for the wholeseller.

(pls, explain it.)
​

Answer 1

$200

Step-by-step explanation:

Given:

Wholeseller sold for 10% of profit.

Retailer sold for 20 % of profit at $264

To find:

cost price for the wholeseller

Method of Solution:

It's a chain selling from one to another till customer. Every seller gain some profit on it.

We will solve every part separately.

Solution:

Final Price is $264 with 20% profit it's mean.

$\textsf{Final Cost Price is} = 264 \times \frac{100}{120} \\ \\ = \cancel{264} \times \frac{10\cancel{0}}{\cancel{12}\cancel{0}} \\ \\ = 22 \times 10 \\ \\ = 220$

Hence, Retailer buy it on $220.

________________________________

Again, Wholeseller sold it on 10% profit it's mean.

$\textsf{Cost Price of Wholeseller} = 220 \times \frac{100}{110} \\ \\ = \cancel{220} \times \frac{100}{\cancel{110}} \\ \\ = 2 \times 100 \\ \\ = 200$

Therefore, Wholeseller Cost Price is $200.

Answer 2

Answer:

☢ Given : A wholeseller sold an article to the retailer at a profit of 10%. The retailer then sold the article to the customer for Rs. 264 at a profit of 20%.

⠀

• Selling Price ( SP ) = Rs. 264
• First Profit ( P₁ ) = 10%
• Second Profit ( P₂ ) = 20%

$\rule{100}{0.8}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf Selling\:Price=Cost\:Price \times \dfrac{100+Profit}{100}\\\\\\:\implies\sf SP=CP \times \dfrac{100+P_1}{100} \times \dfrac{100+P_2}{100}\\\\\\:\implies\sf 264 = CP \times \dfrac{100+10}{100} \times \dfrac{100+20}{100}\\\\\\:\implies\sf 264 = CP \times \dfrac{110}{100} \times \dfrac{120}{100}\\\\\\:\implies\sf 264 = CP \times \dfrac{11}{10} \times \dfrac{6}{5}\\\\\\:\implies\sf 264 \times \dfrac{10}{11} \times \dfrac{5}{6} = CP\\\\\\:\implies\sf 4 \times 10 \times 5 = CP\\\\\\:\implies\underline{\boxed{\sf CP = Rs.\:200}}$

⠀

$\therefore\:\underline{\textsf{Cost Price of article for wholeseller is \textbf{Rs. 200}}}.$

⠀⠀⠀$\rule{160}{1.5}$

$\boxed{\begin{minipage}{6.5 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ \sf SP = CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$