What percent above the cost price of an item should a shopkeeper mark his goods so that after allowing a discount of 30%, he still gains 10%?
40%
If he marks up r%, then
(1+r)c*.70 = 1.1c
1+r = 1.1/.7
r = 1.1/.7-1 = 0.57 = 57% or 4/7
Check:
cost = 14
1.57*14 = 22
22*.7 = 15.4 = 14 * 1.10
To determine the percentage above the cost price that the shopkeeper should mark his goods, we need to set up an equation.
Let's assume the cost price of the item is "x."
The shopkeeper marks the price of the item "p" percent above the cost price.
After allowing a discount of 30%, the selling price will be 70% (100% - 30%) of the marked price.
After allowing a discount and gaining a profit of 10%, the selling price will be 110% (100% + 10%) of the cost price.
Now, we can set up the equation to solve for "p":
x + p% of x = 110% of (70% of (x + p% of x))
To solve this equation, we can follow these steps:
1. Distribute the percentages:
x + (p/100)x = 110% * 70% * (x + (p/100)x)
2. Simplify percentages:
x + (p/100)x = (110/100) * (70/100) * (x + (p/100)x)
3. Simplify fractions:
x + (p/100)x = (77/100) * (x + (p/100)x)
4. Remove percentages and fractions:
100x + px = 77x + 77(p/100)x
5. Combine like terms:
100x - 77x = 77(p/100)x - px
23x = (77p - 100p)x/100
6. Cancel out x:
23 = (77p - 100p)/100
7. Simplify:
23 = -23p/100
8. Cross-multiply:
23 * 100 = -23p
9. Solve for p:
p = -2300 / -23
p = 100
Therefore, the shopkeeper should mark his goods 100% above the cost price, so that after allowing a discount of 30%, he still gains 10%.