Question

A dealer marks his goods $35\%$ above the cost price and then allows $15\%$ discount on it. What is the cost price of an article on which he gains $Rs.88.50$ ?

Answer 1

Let, Cost Price (CP) of the goods be $100$ units

Now, According to question,

Marked Price (MP) $=100+35\%\times 100=135$ units

Now, Selling Price (SP) of the goods $=$ MP $-$ Discount

$\Rightarrow$ SP $=135-15\%\times 135$

$\Rightarrow SP=135-(\frac{15}{100}\times 135)$

$\Rightarrow SP=135-\frac{2025}{100}$

$\Rightarrow SP=135-20.25$

$\Rightarrow SP=114.75$ units ...(1)

$\therefore$ Profit earned $=SP-CP=$114.75-100=14.75$ units

Now, According to question,

$14.75$ units =$Rs.88.50$

$\Rightarrow 1$ unit = $Rs.\frac{88.50}{14.75}$

$\Rightarrow 100$ units = $Rs.\frac{88.50}{14.75}\times 100=Rs.600$

Hence, cost price of the goods is $Rs.600$