I am stuck at a couple of percentage questions.
A merchant sells an item at a 20% discount. But still makes a profit of 20% of the COST. What percentage of the cost would the Gross profit on the item have been if it had been sold without the discount.
At a special sale, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at this rate, the mount saved will be what percent of the original price of the 5 tickets.
On
Let the marked price (on which discount is offered) be x. Selling price = 100% x - 20% x = 80% x = 0.8 x.
Now, selling price = cost price + 20% of cost price.
Selling price = 120/100 * cost price = 1.2 cost price
0.8 x = 1.2 * Cost price
Cost price = 0.8/1.2 x = 2/3 x
Without discount, Selling price = marked price = x.
Profit = selling price - cost price = x - 2/3 x = 1/3 x.
Let gross profit be y% of cost price.
Therefore, (y/100) * 2/3 x = 1/3 x
y/100 = (1/3) * x * (3/2) * (1/x)
y/100 = 1/2
y = 50
Therefore, the profit would have been 50% of the cost without discount.
PROBLEM 2:
Let x be the original cost of each ticket. Price of 5 tickets = 5x
Under the special sale, Price of 5 tickets = Original price of 3 tickets = 3x
Amount saved = 5x - 3x = 2x
Let amount saved be y% of original price of 5 tickets.
therefore, y/100 * (Original price of 5 tickets) = Amount saved.
y/100 * 5x = 2x
Dividing both sides by x
y/100 * 5 = 2
y/20 = 2
y = 40
Therefore, the amount saved will be 40 percent of the original price of the 5 tickets.
Percentage profit P = $\frac{(SP-C)}{C}$
P = $\frac{(0.8SP-C)}{C} = .2$
$.8SP = 1.2C$
$ SP = \frac{1.2}{.8}C = 1.5C$
Without Discount
P = $\frac{(1.5C-C)}{C} = .5 = 50$%
Part 2:
Original Price = P
Amount spent on buying 5 tickets on sale $= 3*P$
Amount spent on one ticket $= \frac{3P}{5}$
Amount spent on one ticket without sale$ = P$
Savings on one ticket $= P-\frac{3P}{5}=\frac{2P}{5}$
Savings on 5 tickets as a percentage of original price $= \dfrac{\frac{2P}{5}.\times 5}{5P}$
Savings on 5 tickets $= 40$%