Question

James bought two articles for Rs 1800. He sold one of them at a profit of 15% and
the other at a loss of 8%. If he received the same amount for each article, find the
cost prices of the articles.​

Answer 1

$\sf\large\underline\purple{Let:-}$

$\rm{\implies The\:cost\:_{(1st\: article)}=x}$

$\rm{\implies The\:cost\:_{(2nd\: article)}=1800-x}$

$\sf\large\underline\purple{To\: Find:-}$

$\rm{\implies The\:cost\:_{(each\: articles)}=?}$

$\sf\large\underline\purple{Solution:-}$

• To calculate the cost price of each article at first we have to find out selling price of each article. Here we have to calculate selling price of both article ap per the given clue in the question:-]

$\sf\small\underline\red{Calculation\:of\:(1st)\: article:-}$

$\sf\small\underline{Here,\:\:CP=x\:\:P=15\%:-}$

$\tt{\implies SP=\dfrac{100+G\%}{100}*CP}$

$\tt{\implies SP=\dfrac{100+15}{100}*x}$

$\tt{\implies SP=\dfrac{115}{100}*x}$

$\tt{\implies SP=\dfrac{115x}{100}}$

$\sf\small\underline\red{Calculation\:of\:(2nd)\: article:-}$

$\sf\small\underline{Here,\:\:CP=1800-x\:\:L=8\%:-}$

$\tt{\implies SP=\dfrac{100-L\%}{100}*CP}$

$\tt{\implies SP=\dfrac{100-8}{100}*1800-x}$

$\tt{\implies SP=\dfrac{92}{100}*1800-x}$

• Now let's focus again in the given Question that James sold the articles at same price it means sp¹=sp² then set up equation after that calculate the value of x then you get the cost price of the article:-]

$\tt{\implies SP\:_{(1st)}=SP\:_{(2nd)}}$

$\tt{\implies \dfrac{115x}{100}=\dfrac{92}{100}*1800-x}$

$\tt{\implies 115x=92*(1800-x)}$

$\tt{\implies 115x=92*1800-92x}$

$\tt{\implies 115x+92x=1800*92}$

$\tt{\implies 207x=165600}$

$\tt{\implies x=800}$

$\sf\large{Hence,}$

$\rm{\implies The\:cost\:_{(1st\: article)}=x=Rs.800}$

$\rm{\implies The\:cost\:_{(2nd\: article)}=1800-x=Rs.1000}$

Answer 2

$\huge \pink \star{ \green{ \boxed{ \boxed{ \boxed{ \orange{ \mathtt{Solution}}}}}}} \pink \star$

$\large\mathtt \red{ \underline{Lets \: Assume:- }}$

$\implies \sf{Cost \: of \: 1st \: article \: as \: x}$

$\implies \mathsf{Cost \: of \: 2nd \: article \: be \: 1800-x}$

$\large\mathtt \red{ \underline{To \: Prove:- }}$

$\implies \sf{Cost \: prices \: of \: the \: articles.}$

$\large\mathtt \red{ \underline{Formula \: to \: be \: used:- }}$

➣Firstly we will find the selling price of each article so that we can calculate the cost price.

$\large\mathtt \red{ \underline{Solution }}$

$\large\mathtt{➣Article \: 1:- }$

• Cost Price:- x
• Profit :- 15%

$\implies \mathtt{S.P. :- \frac{100 + profit}{100} } \times \mathtt c \mathtt p$

$\implies \mathtt{S.P. :- \frac{100 + 15}{100} } \times \mathtt x$

$\implies \mathtt{S.P. :- \frac{115x}{100} }$

$\large\mathtt{➣Article \: 2:- }$

• Cost Price:- 1800-x
• Loss :- 8%(-8)

$\implies \mathtt{ S.P.:- \frac{100 - loss}{100} } \times \mathtt c \mathtt p$

$\implies \mathtt{ S.P.:- \frac{100 - 8}{100} } \times \mathtt {1800 - x}$

$\implies \mathtt{ S.P.:- \frac{92}{100} } \times \mathtt {1800 - x}$

$\large\mathtt{➣So \: now:-}$

$\mathtt{S.P \: of \: article \: 1 = S.P. \: of \: article \: 2}$

$\implies \mathtt{ \frac{115x}{100} = \frac{92}{100} \times 1800 - x}$

• As 100 will get cancelled.

$\implies \mathtt{115x = 92 \times 1800 - x}$

$\implies \mathtt{115x = 92 \times 1800 - 92x}$

$\implies \mathtt{115x + 92x = 92 \times 1800 }$

$\implies \mathtt{207x = 165600 }$

$\implies \mathtt{x = 800}$

$\large\mathtt{➣Therefore:- }$

• Cost of 1st article:- x = 800
• Cost of 2nd article:- 1800-x = 1800-800 =1000