When an article is sold at a discount of 10%, a profit of Rs 8 is earned. If the article is sold without allowing a discount, there will be a profit of Rs 20. Find the cost price of the article.

Solution:

Let the marked price of the article be MP.

Condition I,

discount percentage (d%) = 10%

profit amount (P) = Rs 8

We know,

SP1 = $MP ( 1 - \frac{d%}{100})$

$= MP ( 1 - \frac{10}{100})$

$= MP × \frac{9}{10}$

$= \frac{9MP}{10}$

And,

CP1 = $SP - P$

$= \frac{9MP}{10} - 8$

Condition II,

discount percentage (d%) = 0

Profit amount (P2) = Rs 20

We know, when there is no discount,

$SP = MP$

So, CP2 = $SP - P2$

$= MP - 20$

In both the conditions, Cost Price of the article remains the same.

$or, CP1 = CP2$

$or, \frac{9MP}{10} - 8 = MP - 20$

$or, 20 - 8 = MP - \frac{9MP}{10}$

$or, 12 = \frac{10MP - 9MP}{10}$

$or, 12 × 10 = MP$

$\therefore MP = Rs 120$

Now, put value of MP in CP2 to get CP

CP2 = $120 - 20$

$= Rs 100$

Hence, the required cost price of the article is Rs 100.