Question

An article is sold at 25% profit. If the CP and the SP of the article are increased by Rs 60 and Rs 30 respectively, the profit% decreases by 15%. Find the cost price of the article. ​

Answer 1

$i ) Let \: cost \:price \: of \: an \: article (c.p) = x$

$Selling \:price = s.p.$

$Profit (g) = 25\%$

$\boxed {\pink { s.p = c.p\Big( \frac{100+g}{100} \Big) }}$

$\implies s.p = x\Big( \frac{100+25}{100} \Big) \\= x \times \frac{125}{100} \\= \frac{5x}{4} \: --(1)$

/* According to the problem given */

The SP of the article are increased by Rs 60 and Rs 30 respectively, the profit% decreases by 15%.

$New \: c.p = ( x + 60 )$

$New \:s.p = \Big( \frac{5x}{4} + 30 \Big)$

$Loss (l) = 15\%$

$\boxed { \blue{ s.p = c.p\Big( \frac{100-l}{100} \Big) }}$

$\implies \Big( \frac{5x}{4} + 30 \Big) = (x+60) \Big( \frac{100-15}{100} \Big)$

$\implies \frac{5x+120}{4} = (x+60) \times \frac{85}{100}$

/* Multiplying bothsides by 4, we get */

$\implies 5x + 120 = \frac{85}{25} (x+60)$

$\implies 5x + 120 = \frac{17}{5} (x+60)$

$\implies 5(5x+120) = 17(x+60)$

$\implies 25x + 600 = 17x + 1020$

$\implies 25x - 17x = 1020 - 600$

$\implies 8x = 420$

$\implies x = \frac{420}{8}$

$\implies x = 52.50$

Therefore.,

$\red { Cost \:price \: of \: the \: article }\\ \green {= Rs \: 52.50}$

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