Question

31. A trader marked up the price of a product by 75%.
When the discount was decreased from 50% to 25%,
his profit increased by 210. What is the cost of the
product?
​

Answer 1

$Let \: the \:cost \:price \:of \:the \: product = Rs \:100$

$Marked \:price \:of \:the \: product (m.p) \\= c.p + 75\% \: of \: c.p \\= 100 + 75 \\= Rs \: 175$

$If \: the \: discount \: ( d_{1} ) = 50\%$

$Selling \:price (s.p_{1}) = m.p \Big( \frac{100-discount}{100}\Big) \\= 175\Big( \frac{100-50}{100}\Big) \\= 175 \times \frac{50}{100} \\= Rs\:87.50$

$If \: the \: discount \: ( d_{2} ) = 25\%$

$Selling \:price (s.p_{2}) = m.p \Big( \frac{100-discount}{100}\Big) \\= 175\Big( \frac{100-25}{100}\Big) \\= 175 \times \frac{75}{100} \\= Rs\:131.25$

$Difference \: selling \:price = s.p_{2} - s.p_{1} \\= Rs \:131.25 - Rs \: 87.50 \\= Rs \:43.75$

$Difference \:Rs\: 43.75 \: for \:c.p \: Rs \:100 \\</p><p>Difference \: Rs \: 210 \: for \: c.p = ?$

$\red{Cost \:price \:of \:the \: product} \\= \frac{210 \times 100}{43.75 } \\= Rs \: 480$

/* According to the problem given */

$\red{Cost \:price \:of \:the \: product} \green {= Rs \: 480}$

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