Problem Solving

Ms. Adams sold two properties,X and Y for $30,000 each. She sold property X for 20 percent more than she paid for it and sold property Y for 20 percent 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 $1250
B Loss of $2500
C Gain of $1250
D Gain of $2500
E No Gain No Loss

This question is from powerprep test1, I need explanation for this answer

30000 = 1.2X , X is the original price of property x
30000 = 0.8Y , Y is the original price of property y

Therefore, X = 25000 and Y = 37500

Total Cost price of two properties = 62500
Total Selling price of two properties = 60000

therefore, Loss of 2500

B

I understand that this question can be done by the method mentioned above working with the old and new values. However there is a formula for finding percentage change -

x+y+xy/100 (+ sign is used for profit and - for loss)

for example- The length of a rectangle increased by 40% and width decreased by 30%. Resulting area is what % increase or decrease by original area?

By applying the formula here -
=40-30-1200/100
=40-30-12
=-2 (- means loss)
so 2% decrease from the orginal

but when I tried to apply the same formula in the given question here, it doesnt work...
I did it using the formula as below -

20% increase and then 20% decrease on two items consecutively....

so 20-20-400/100
= 20-20-4
= -4 (which means 4% loss)

so 4% of 60,000 is 2400
means loss of 2400
but the actual answer coming is loss of 2500

Can someone please help me understand where am I going wrong? Thanks.

bharti06 wrote:I understand that this question can be done by the method mentioned above working with the old and new values. However there is a formula for finding percentage change -

x+y+xy/100 (+ sign is used for profit and - for loss)

for example- The length of a rectangle increased by 40% and width decreased by 30%. Resulting area is what % increase or decrease by original area?

By applying the formula here -
=40-30-1200/100
=40-30-12
=-2 (- means loss)
so 2% decrease from the orginal

but when I tried to apply the same formula in the given question here, it doesnt work...
I did it using the formula as below -

20% increase and then 20% decrease on two items consecutively....

so 20-20-400/100
= 20-20-4
= -4 (which means 4% loss)

so 4% of 60,000 is 2400
means loss of 2400
but the actual answer coming is loss of 2500

Can someone please help me understand where am I going wrong? Thanks.

she got loss on the value she invested. so your calculation should 4% of 62500 not 60000.

Also you don't have money she invested so instead of going with such a tedious calculation remember this shot trick, "whenever a person sell two things at price X; one with Y% profit and other with Y% loss, there is always loss of y^2/100.

so when you apply this trick over here you'll get 20^2/100 i.e. 4% loss.


60000 = 96% of X => X = 62500.

Hope this helps.

Kudos,
Hemant

Looks like the math is right above. The key is to realize that you are starting from different bases. The base on the loss will be larger, so net you will have a loss. This is a good first step for eliminating answers.

hemant_rajput wrote: she got loss on the value she invested. so your calculation should 4% of 62500 not 60000.

Also you don't have money she invested so instead of going with such a tedious calculation remember this shot trick, "whenever a person sell two things at price X; one with Y% profit and other with Y% loss, there is always loss of y^2/100.

so when you apply this trick over here you'll get 20^2/100 i.e. 4% loss.


60000 = 96% of X => X = 62500.

Hope this helps.

Kudos,
Hemant

@hemant....
you hit the nail on the head....I should have calculated loss on her investment rather than on selling price...thanks for pointing and thanks so much for the trick as well....much appreciated!!!