How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 15% on the marked price, he gains 8%?
let the rate be r
(.85)r = 1.08
r = 1.08/.85 = 1.2706 or 27.1%
check:
suppose an item costs $100
after markup , cost = 127.10
discount = 127.1(.15) = 19.065
selling price = 108.035
profit = 8.035
percent profit = 8.035/100 = .08035 or appr 8%
To find out how much percent above the cost price the shopkeeper should mark his goods, we can use the following approach:
Let's assume the cost price of the goods is 'CP'.
We need to find the percentage above the cost price at which the goods should be marked. Let's assume this markup percentage as 'x'.
According to the information provided in the question:
1. After allowing a discount of 15% on the marked price, the shopkeeper gains 8%.
Now, let's break down the problem into steps:
Step 1: Calculate the selling price (SP) after allowing a discount of 15%.
SP = Marked price - Discount
SP = (100% + x%) - 15%
SP = (100 + x - 15)% (Equation 1)
Step 2: Calculate the profit percentage.
Profit% = (Profit / CP) * 100
Since the shopkeeper gains 8% from the cost price (CP), profit% = 8%
Step 3: Calculate the selling price (SP) using the profit percentage.
SP = CP + Profit
SP = CP + (8% of CP)
SP = (108/100) * CP (Equation 2)
Step 4: Equate Equation 1 and Equation 2.
(100 + x - 15)% = (108/100) * CP
Simplifying this equation will give us the value of 'x', which is the markup percentage.
Let's calculate it:
(100 + x - 15)% = (108/100) * CP
85 + x = (108/100) * CP (Reduced the percentage symbols)
85 + x = (27/25) * CP (Divided 108 by 100)
x = (27/25) * CP - 85 (Isolated 'x' on one side)
So, the markup percentage 'x' above the cost price should be:
x = (27/25) * CP - 85
To find the exact value of 'x', we need to know the cost price (CP) of the goods.