Question

By selling an article for ₹ 240, a man makes a profit of 20% .
i) What is the cost price of the article ?
ii) What would be his profit percent if he sells the article for
₹ 275?

Answer 1

$\large {\underline {\underline {\textsf{\textbf{Given:}}}}}$

Given that :

• Man sells article for Rs.240 and makes a profit of 20%.

$\large \underline {\underline {\textsf{\textbf{To\: find:}}}}$

We have to find the following :

• CP of the article.
• Profit% if he sells it at Rs.275.

$\large \underline {\underline {\textsf{\textbf{Solution:}}}}$

• Finding CP of the article :

Let the CP of the article be y.

SP of the article = Rs.240

$\: \: \: \: \: \: \: \: \: \: \: \: \underline {\boxed{\pmb{\sf{CP+Profit=Rs.240}}}}$

$\sf : \: \mapsto y+ 20\% \times y = 240$

$\sf : \: \mapsto y+ \cfrac{20}{100} \times y=240$

$\sf : \: \mapsto y+ \cfrac{20y}{100} = 240$

Taking LCM for 100 and y and solving it further :

$\sf : \: \mapsto \cfrac{100y+20y}{100} = 240$

$\sf : \: \mapsto \cfrac{120y}{100} = 240$

$\sf : \: \mapsto 120y=240(100)$

$\sf : \: \mapsto y=\cancel{ \cfrac{24000}{120}}$

$\sf : \: \mapsto y=200$

$\: \: \: \: \: \: \: \: \: \underline{\boxed{\pmb{\sf{\therefore \: CP \: of \: the \: article=Rs.240.}}}}$

We know that,

• SP - CP = Profit

$\sf : \: \mapsto Rs .275 - Rs.200$

$\sf : \: \mapsto Rs.75$

• Finding profit% if the article is sold at Rs.275 :

$\: \: \: \: \: \: \: \: \: \underline {\boxed {\pmb{\sf{Profit\%= Profit \times \frac{100}{CP} }}}}$

$\sf : \: \mapsto70 \times \cfrac{1\cancel{00}}{2\cancel{00}}$

$\sf : \: \mapsto 75 \times \cfrac{1}{2}$

$\sf : \: \mapsto37.5$

$\: \: \: \: \: \: \: \: \: \underline {\boxed {\pmb{\sf{\therefore \: Profit\%=37.5\%}}}}$