Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
(A) Loss of $1,250
(B) Loss of $2,500
(C) Gain of $1,250
(D) Gain of $2,500
(E) Neither a net gain nor a net loss
Hi Roland2rule,
Lets take a look at your question.
Let the property X has original value of $x, then, it sale price i.e. $30,000 at 20% profit can be represented as:
$$x\ +\ \left(20\%\right)x=30,000$$
$$x\ +\ \left(\frac{20}{100}\right)x=30,000$$
$$x\ +\ \left(0.2\right)x=30,000$$
$$1.2x=30,000$$
$$x=\frac{30,000}{1.2}$$
$$x=25,000$$
Therefore, original price of property X is $25,000 and it was sold at $30,000.
Profit Gained = $30,000 - $25,000 = $5,000
Let the property Y has original value of $y, then, it sale price i.e. $30,000 at 20% loss can be represented as:
$$y\ -\ \left(20\%\right)y=30,000$$
$$y\ -\ \left(\frac{20}{100}\right)y=30,000$$
$$y\ -\ \left(0.2\right)x=30,000$$
$$0.8x=30,000$$
$$x=\frac{30,000}{0.8}$$
$$x=37,500$$
Therefore, original price of property Y is $37,500 and it was sold at $30,000.
Loss = $37,500 - $30,000 = $7,500
There is a gain of $5,000 in property X and loss of $7,500 in property Y.
The loss is greater than the profit, so to find the total loss we will subtract the profit from the loss.
Loss = 7,500 - 5,000 = $2,500
Therefore, Option
B is correct.
Hope this helps.
I am available, if you'd like any follow up.
