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 9,492 with 13% VAT to buy the article, by what percent is the marked price above the cost price of the article?
percent/100 = p
[ (1+p) * cost ] [ 1-.16 ] = cost * 1.05
[ cost * 1.05 ] 1.13 = 9492
[ cost * 1.05 ] = 9492/1.13 = 8400
cost = 8400/1.05 = 8000
[ (1+p) * 8000] [ 1-.16 ] = 8400
[ (1+p) * 8000 ] = 8400/.84 = 10,000
1+p = 1.25
p = .25
percent = 100 p
To find the percent by which the marked price is above the cost price, we will use a step-by-step approach.
Step 1: Let's assume the cost price of the article is 'C'.
Step 2: The shopkeeper marked the price a certain percent above the cost price. Let's assume this percent is 'P'. Therefore, the marked price is given by (C + (P/100) * C).
Step 3: The shopkeeper allowed a 16% discount, which means the customer paid (100 - 16)% = 84% of the marked price. So, the selling price after discount is (84/100) * (C + (P/100) * C).
Step 4: The shopkeeper wants to make a 5% profit, so the selling price after discount should be equal to (1 + (5/100)) * C.
Step 5: Including a 13% VAT, the final amount paid by the customer is (1 + (13/100)) times the selling price after discount.
Now, we can set up the equation and solve for 'P':
(1 + (13/100)) * [(84/100) * (C + (P/100) * C)] = (1 + (5/100)) * C
Simplifying the equation:
(113/100) * [(84/100) * (C + (P/100) * C)] = (105/100) * C
(113/100) * (84/100) * (C + (P/100) * C) = (105/100) * C
(113/100) * (84/100) = (105/100) * (1 + (P/100))
(113 * 84) / (100 * 100) = (105 * (100 + P)) / 100
95052 / 10000 = (10500 + 105P) / 100
Solving for P:
10500 + 105P = 950.52
105P = 950.52 - 10500
105P = -9549.48
P = -9549.48 / 105
P ≈ -91.00
Therefore, the marked price is approximately 91% below the cost price of the article.