A trader fixed the price of cosmetic items 30% above the cost price. When he/she sold an item at 25% discount, there was a loss of Rs 15. Find the cost price and marked price of the item.

Question: A trader fixed the price of cosmetic items 30% above the cost price. When he/she sold an item at 25% discount, there was a loss of Rs 15. Find the cost price and marked price of the item.

Solution:

Let MP be the marked price, CP be the cost price, SP be the selling price and d be the discount.

According to the question,

discount percentage (d%) = 25%

loss amount (L) = Rs 15

Here,

MP = CP + 30% of CP

$= CP ( 1 + \frac{30}{100})$

$= CP × \frac{130}{100}$

$or, MP = \frac{13CP}{10}$ - (i)

And,

SP = MP ( 1 - \frac{d%}{100})$

$= MP ( 1 - \frac{25}{100})$

$= MP × \frac{75}{100}$

$= \frac{13 CP}{10} × \frac{3}{4}$

$= \frac{39 CP}{40}$

Given,

Loss = Rs 15

$or, CP - SP = 15$

$or, CP - \frac{39CP}{40} = 15$

$or, \frac{40CP - 39CP}{40} = 15$

$or, CP = 15 × 40$

$\therefore CP = Rs 600$

Put value of CP in equation (i), we get,

$or, MP = \frac{13 × 600}{10}$

$\therefore MP = Rs 780$

Hence, the required cost price and marked price of the article are Rs 600 and Rs 780, respectively.