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percentage and interest

This topic has 2 expert replies and 0 member replies

percentage and interest

Post Sat Sep 30, 2017 7:47 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

    Is there any detailed and straight forward approach to this question? qa is b

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    Post Sun Oct 01, 2017 2:52 am
    Roland2rule wrote:
    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
    Since the selling price of $30,000 is 20% more than the cost price of X, the selling price of $30,000 is equal to 120% of the cost price of X:
    30,000 = (120/100)X
    30,000 = (6/5)X
    (5/6)(30,000) = X
    X = 25,000.

    Since the selling price of $30,000 is 20% less than the cost price of Y, the selling price of $30,000 is equal to 80% of the cost price of Y:
    30,000 = (80/100)Y
    30,000 = (4/5)Y
    (5/4)(30,000) = Y
    Y = 37,500.

    Sum of the cost prices = 25,000 + 37,500 = 62,500.
    Sum of the selling prices = 30,000 + 30,000 = 60,000.
    Net loss = (sum of the cost prices) - (sum of the selling prices) = 62,500 - 60,000 = 2500.

    The correct answer is B.

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    Post Fri Oct 13, 2017 9:51 am
    Quote:
    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.

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