A retailer bought an item for RM40 less 10% and 5%.If the retailer intends to make a gross profit of 25% of the cost by selling the item at a 60% discount,find the list price.
I will assume cost price is 40 less 10%,5%
so actual cost price = 40(.9)(.95) = 34.20
let list price be x
.4x = 34.20(1.25)
x = 34.20(1.25)/.4 = 106.875
I interpreted "25% of the cost" as the actual cost, not the stated RM40 less 10%, 5% "
check:
60% discount on 106.875 = 64.125
for a selling price of 106.875-64.125 = 42.75
profit = 42.75 - 34.20 = 8.55
percentage profit = 8.55/34.2 = .25 or 25%
All works out.
To find the list price, we need to calculate the cost price first. Let's start by finding the original price after a 10% discount.
Step 1: Calculate the price after the first discount.
Original price - 10% of original price.
Let x be the original price.
x - 0.10x = x(1 - 0.10) = 0.90x
Step 2: Calculate the price after the second discount.
0.90x - 5% of 0.90x.
0.90x - 0.05(0.90x) = x(1 - 0.05) - 0.045x = 0.95x - 0.045x = 0.905x
Step 3: Calculate the cost price after the retailers bought the item for RM40 less.
0.905x - RM40
Step 4: Calculate the selling price to make a gross profit of 25%.
Cost price + 25% of cost price.
(0.905x - RM40) + 0.25(0.905x - RM40) = 0.905x - RM40 + 0.22625x - RM10 = 1.13125x - RM50
Step 5: Calculate the selling price after a 60% discount.
1.13125x - RM50 - 60% of (1.13125x - RM50).
1.13125x - RM50 - 0.60(1.13125x - RM50) = 1.13125x - RM50 - 0.67875x + RM30 = 0.4525x - RM20
Since the selling price is 60% of the list price, we can set it equal to 0.60 times the list price.
0.4525x - RM20 = 0.60x
Now we can solve for x, which represents the list price.
0.60x - 0.4525x = RM20
0.1475x = RM20
x = RM20 / 0.1475
x ≈ RM135.59
Therefore, the list price of the item is approximately RM135.59.