Question: Mrs. Sharma fixed the price of a pen to make a profit of 10%. But she sold it allowing a discount of Rs 7.50 and lost 5%. At what price did she purchase the pen?

Solution:

For a pen,
Let the marked price of the pen be MP.

Condition I,
Profit percentage (p%) = 10%
Since there is no discount, MP = SP1

$CP_1 = \dfrac{SP1}{1 + \frac{p%}{100}}$

$= \dfrac{MP}{1 + \frac{10}{100}}$

$= \dfrac{MP}{\frac{110}{100}}$

$= \dfrac{MP}{\frac{11}{10}}$

$= \dfrac{10MP}{11}$


Condition II,
discount amount (d) = Rs 7.50
Loss percentage (l%) = 5%

Selling Price (SP2) = $MP - d$
$= MP - 7.50$

$CP2 = \dfrac{SP2}{1 - \frac{l%}{100}}$

$= \dfrac{MP - 7.50}{1 - \frac{5}{100}}$

$= \dfrac{MP - 7.50}{\frac{95}{100}}$

$= \dfrac{(MP - 7.50)20}{19}$


WE KNOW,
Cost price in both the cases (conditions) are the same.
i.e. CP1 = CP2

$or, \dfrac{10MP}{11} = \dfrac{(MP - 7.50)20}{19}$

$or, 10MP × 19 = (20MP - 150)11$

$or, 190MP = 220MP - 1650$

$or, 1650 = 220MP - 190MP$

$or, 1650 = 30MP$

$\therefore MP = Rs 55$


Put value of MP in CP1, we get,
CP1 = $\dfrac{10 × 55}{11}$

$= Rs 50$


Therefore, the required marked price of the pen is Rs 50.