When an article was sold at a discount of 10%, a customer paid Rs 9,153 with 13% VAT. If 8% profit was made in this transaction by how many percent was the marked price above the cost price?

Question: When an article was sold at a discount of 10%, a customer paid Rs 9,153 with 13% VAT. If 8% profit was made in this transaction by how many percent was the marked price above the cost price?

Solution:

For an article

discount percentage (d%) = 10%

VAT percentage (VAT%) = 13%

Profit percentage (P%) = 8%

SP with VAT = Rs 9153

We know,

SP = $\dfrac{SP with VAT}{100 + \frac{VAT%}{100}$

$= \dfrac{9153}{100 + \frac{13}{100}}$

$= \dfrac{9153}{ \frac{113}{100}}$

$= 9153 × \dfrac{100}{113}$

$= Rs 8100$

And,

MP = $\dfrac{SP}{100 - \frac{d%}{100}}$

$= \dfrac{8100}{100 - \frac{10}{100}}$

$= \dfrac{8100}{\frac{90}{100}}$

$= 8100 × \frac{10}{9}$

$= Rs 9000$

Now,

CP = $\frac{SP}{1 + \frac{P%}{100}}$

$= \frac{8100}{1 + \frac{8}{100}}$

$= \frac{8100}{\frac{108}{100}}$

$= 8100 × \frac{100}{108}$

$= Rs 7500$

So,

We have to find the difference in comparison to the cost price. So, we divide the obtained difference by Cost Price and not by the Marked Price.

Percentage = $\dfrac{MP - CP}{CP } × 100%$

$= \dfrac{9000 - 7500}{7500} × 100%$

$= \dfrac{1500}{7500} × 100%$

$= 20%$

Hence, the markedd price is 20% above the cost price in the above condition.