Question

2. The marked price of an article is Rs 500. The
-shopkeeper gives a discount of 5% and still makes
à profit of 25%. Find the cost price of the article
​

Answer 1

Given :

• Marked Price ( MP)= Rs 500
• Discount % = 5%
• Profit % = 25%

To Find :

• The cost price (CP) of the article.

Solution :-

Finding Discount :

$\bigstar{\boxed {\tt{Discount = Discount \% \:of\: MP}}}\bigstar$

$: \implies{\sf{Discount =Discount \% \:of\: MP}} \\ \\ : \implies{\sf{Discount =5\% \:of\: Rs \: 500}} \\ \\ : \implies{\sf{Discount = Rs \:( 500 \times \dfrac{5}{100} )}} \\ \\ : \implies{\sf{Discount = Rs \:( 5 \times 5)}} \\ \\ : \implies{ \boxed{\tt{Discount = Rs \:25}}}$

Finding SP :

$\bigstar{\boxed {\tt{ SP= MP - Discount}}}\bigstar$

$: \implies {\sf{ SP= MP - Discount}} \\ \\ : \implies {\sf{ SP= Rs \:(500 - 25)}} \\ \\ : \implies{ \boxed {\tt{ SP= Rs \:475}}}$

Finally Finding CP :

$\bigstar { \boxed{\tt{CP = \dfrac{100}{(100 + profit\%)} \times SP}}}\bigstar$

$: \implies{\sf{CP = \dfrac{100 }{(100+profit\%)}\times SP}} \\ \\ : \implies{\sf{CP = Rs\:[\dfrac{100 }{(100+ 25)} \times 475]}}\\ \\ : \implies{\sf{CP = Rs \:(\dfrac{100 }{125} \times 475)}}\\ \\ : \implies{\sf{CP = Rs \:(\dfrac{47500 }{125} )}} \\ \\ : \implies{ \boxed{\tt{CP = Rs \:380}}}$

$\underline {\bf{\therefore{The \: cost \: price \: of\: the \:article \:is\:Rs \:380.}}}$

Answer 2

Given :-

• Marked price (MP) = Rs.500
• Discount % = 5%
• Profit % = 25%

To Find :-

• The cost price(CP) of the article.

Solution :-

Case(1) :- Finding Discount,

Discount =Discount % of MP

↪Discount = 5/100 × 500

↪Discount = 5 × 5

↪Discount = Rs. 25

Case(2) :- Finding Selling Price(SP),

SP = MP - Discount

↪SP = 500 - 25

↪SP = Rs. 475

Case(2) :- Finding Cost Price(CP),

CP = 100(100 + Profit%) × SP

↪CP = 100/(100 + 25) × 475

↪CP = 100/125 × 475

↪CP = 100 × 3.8

↪CP = Rs. 380

Hence,

• The cost price of an article is Rs. 380.