Question

A shopkeeper purchased a bicycle for Rs 5,000 and marked its price a certainpercent above the cost price. Then, he sold it at 10% discount. If a customer paidRs 6,356.25 with 13% VAT to buy it, how many percent is the marked price abovethe cost price?

Answer 1

The final cost of the bicycle with VAT included was Rs 6,356.25. Since the VAT was 13% the price before taxes is:

`\begin{gathered} (113)/(100)\text{ = }(6356.25)/(x) \\ 113\cdot x\text{ = 635625} \\ x\text{ = }(635625)/(113)\text{ = 5625} \end{gathered}`

The costumer got a 10% discount to reach that value, therefore the price marked up by the seller before the discount can be found by applying a rule of three as shown below:

`\begin{gathered} (5625)/(x)\text{ = }(90)/(100) \\ 90x\text{ = 562500} \\ x\text{ = }(562500)/(90)=\text{ }6250 \end{gathered}`

We now know the price at which the seller marked up the bicycle and we want to find which percentage it represents compared to the cost price. To do that we will find the absolute difference in value and apply a rule of three.

`\text{absolute difference = 6250 - 5000 = }1250`

Applying the rule of three:

`\begin{gathered} (5000)/(1250)\text{ = }(100)/(x) \\ 5000\cdot x\text{ = 100}\cdot1250 \\ x\text{ = }(125000)/(5000)\text{ = 25} \end{gathered}`

The price was marked up 25% above the cost of the bicycle.