A shopkeeper marked the price of an article a certain percent above the cost price and he allowed 16% discount to make 5 % profit. if a customer paid rs 9492 with 13% vat to buy the article , by what percent did he mark the MP above CP
1 + 13%
1 + 0.13 = 1.13
9492 / 1.13 = 8400
1 + 5%
1 + 0.05 = 1.05
8400 / 1.05 = 8000
8400 = (1 - 0.16)800x
8400 = (0.84)800x
8400 = 6720x
8400 / 6720 = 6720x / 6720
1.25 = x ; 25% was percent
sorry I meant 8000x
To find the percentage at which the shopkeeper marked the article's selling price (MP) above the cost price (CP), we can solve this problem step by step:
Step 1: Calculate the original CP.
Let's assume the original CP of the article is 'x' rupees.
Step 2: Calculate the marked price (MP) before the discount.
Since the shopkeeper marked the price 'a certain percent' above the cost price, we can calculate the MP as follows:
MP = CP + (certain percent of CP)
MP = x + (certain percent/100) * x
Step 3: Calculate the discounted price.
Given that the shopkeeper allowed a 16% discount to make a 5% profit, we can calculate the discounted price as follows:
Discounted price = MP - (16/100) * MP
Discounted price = MP * (1 - 16/100)
Discounted price = MP * (84/100)
Step 4: Calculate the selling price (SP) including VAT.
The selling price after applying VAT can be calculated as follows:
SP = Discounted price + (13/100) * Discounted price
SP = Discounted price * (1 + 13/100)
SP = Discounted price * (113/100)
According to the problem, the customer paid Rs 9492, so we equate SP to 9492 and solve for Discounted price.
9492 = Discounted price * (113/100)
By solving the equation, we find the value of the Discounted price.
Step 5: Calculate the percentage at which the MP is marked above the CP.
Once we have the Discounted price, we can calculate the MP by using Step 3:
MP = Discounted price / (84/100)
Finally, let's calculate the percentage at which the MP is marked above the CP:
Percentage = ((MP - CP) / CP) * 100
By substituting the values of MP and CP, we can find the required percentage.