Question

An article is sold at $20\%$ profit. If is cost price is increased by Rs. $50$ and at the same time if its selling price is also increases by Rs. $30$ , the percentage of profit decrease by $\frac{10}{3}\%$. Find the cost price approximately.

• A. $500$
• B. $850$
• C. $700$
• D. $800$

Answer 1

Answer: (B)

$850$

Let initial cost price be Rs. $x$

Profit $=$ $\frac{20}{100}\times x=\frac{x}{5}$

So, Selling price $=$ $x+\frac{x}{5}=\frac{6x}{5}$

New cost price $=$ $x+50$

New selling price $=$ $\frac{6x}{5}+30$

New profit $=$ $(\frac{6x}{5}+30)-(x+50)=\frac{x}{5}-20$

$\text{Profit}\%=\frac{\frac{x}{5}-20}{(x+50)}\times 100$

According to the question profit $\%=$ $(20-\frac{10}{3})\%=\frac{50}{3}\%$

So, $\frac{\frac{x}{5}-20}{x+50}\times 100=\frac{50}{3}$

$\Rightarrow$ $\frac{x-100}{5(x+50)}\times 100=\frac{50}{3}$

$\Rightarrow$ $\frac{x-100}{x+50}=\frac{5}{6}$

$\Rightarrow$ $6x-600=5x+250$

$\Rightarrow$ $x=850$

Therefore, cost price of article is Rs. $850$.