Question

Cost price of articles A and B are Rs. 360 and Rs. 400 respectively. Article A was sold at a profit of 15% and article B was sold at a loss of ‘X’%. If the overall loss incurred after selling both the articles is Rs. 74, what is the value of ‘X’ ?

Answer 1

Case 1:

Cost price of article A = Rs 360,

profit (g) = 15% ,

$Selling \:price \:of \:A = c.p\big( \frac{100+g}{100}\big) \\= 360 \big( \frac{100+15}{100}\big) \\= 360\times \frac{115}{100}\\= Rs\:414$

Case 2:

Cost price of article B = Rs 400,

Loss (l) = x% ,

$Selling \:price \:of \:B= c.p\big( \frac{100-l}{100}\big) \\= 400 \big( \frac{100-x}{100}\big) \\= 4(100-x) \\= 400 - 4x$

$Total \:cost \:price = Rs \:360 + Rs\: 400 \\= Rs\:760$

$Total \: selling \:price = Rs \:414 + Rs\:(400-4x)\\= 814 - 4x$

/* According to the problem given */

$Total \: Loss = Rs \:74$

$\implies 760 - (814-4x) = 74$

$\implies 760 - 814 + 4x = 74$

$\implies -54 + 4x = 74$

$\implies 4x = 74 + 54$

$\implies 4x = 128$

$\implies x = \frac{128}{4}$

$\implies x = 32$

Therefore.,

$\red { Value \:of \:x }\green { = 32\% }$

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