A shopkeeper marked the price of an article certain precent above the cost price and he allowed 16% discount to make 5% profit if a costumber paid rs 9492 with 13% VAT to buy the article .by what present is the marked price above the cost price of the article .
If he raised the price by x%, then if the cost was c, he sold it for
c(1 + x/100)
Then, after the 16% discount, his sales price was 5% above cost, so
c(1 + x/100) * 0.84 = 1.05c
Or, dividing by c,
(1 + x/100) * 0.84 = 1.05
x = 25
So, he raised his price by 25%
Now see what you can do with the rest.
Please solve it. Thank you
To find the percentage by which the marked price is above the cost price, we need to understand the given information and calculate the solution step by step.
Let's assume the cost price of the article is "C."
According to the given information:
1. The shopkeeper marked the price of the article a certain percentage above the cost price.
2. The shopkeeper allowed a 16% discount on the marked price.
3. The resulting discounted price includes a 13% VAT.
4. The shopkeeper aims to make a 5% profit.
First, let's find the selling price after the discount and VAT:
1. Selling Price after Discount:
The shopkeeper allowed a 16% discount, so the selling price after the discount can be calculated as:
Selling Price = Marked Price - (Discount % * Marked Price)
Selling Price = Marked Price - (16/100 * Marked Price)
= Marked Price (1 - 16/100)
= Marked Price * (84/100)
2. Selling Price after VAT:
The final selling price after adding 13% VAT can be calculated as:
Selling Price = Selling Price + (VAT % * Selling Price)
Selling Price = Selling Price + (13/100 * Selling Price)
= Selling Price (1 + 13/100)
= Selling Price * (113/100)
Now, let's find the selling price after all the calculations:
Selling Price = 9492 (as given in the question, the customer paid this amount)
Therefore, we can write the equation as:
Selling Price * (113/100) = 9492
Solving this equation will give us the value of Selling Price.
Next, let's find the cost price (C) using the given information of the 5% profit:
Profit Percentage = (Selling Price - Cost Price) / Cost Price * 100
5% = (Selling Price - C) / C * 100
Solving this equation will give us the value of C (Cost Price).
Finally, to find the percentage by which the marked price is above the cost price, we can use the formula:
Percentage Above Cost Price = (Marked Price - Cost Price) / Cost Price * 100
By substituting the values of Marked Price and Cost Price obtained from the equations above, we can calculate the solution.