A shopkeeper purchased a bicycle for Rs 5000 and marked its price a certain percent above the cost price. Then, he sold it at 10% discount. If a customer paid Rs 6356.25 with 13% VAT to buy it, how many percent is marked price above the cost price?

Solution:

Here,

Cost price (CP) = Rs 5000

Discount percentage (d%) = 10%

VAT % = 13%

SP with VAT = Rs 6356.25

We know,

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

$= \dfrac{6356.25}{100 + \frac{13}{100}}$

$= \dfrac{6356.25}{\frac{113}{100}}$

$= 6356.25 × \frac{100}{113}$

$= Rs 5625$

And,

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

$= \dfrac{5625}{1 - \frac{10}{100}}$

$= \dfrac{5625}{\frac{90}{100}}$

$= 5625 × \frac{100}{90}$

$= Rs 6250$

Now,

Comparing MP and CP,

$= \dfrac{MP - CP}{CP} × 100%$

$= \dfrac{6250 - 5000}{5000} × 100%$

$= \dfrac{1250}{50} %$

$= 25%$

Hence, the marked price is 25% more than that of the cost price.