Problem Solving

2 items are sold at same price d$.

One item is sold at gain of x%

Other item is sold at loss of x%

What is the overall loss%?

we can solve this by plugging the numbers.

Let the SP of each item be 120 and x=20%

First Item:

SP=120

This item is sold at the gain of 20%

-->CP=100


Second Item:

SP=120

This item is sold at the loss of 20%

-->CP=150

Total SP=240,Total CP=250

Total Loss=4%

By substituting x=20 in answer options verify which option satisfy the value[4%]

Option B

(20*20)/(100*100)=4%

Hope this clarify...

aarati wrote:i still could n't get this................can someone make it clear..

First up, this formula isn't of much use if the percent gain or loss in the two items purchased is different for the two items. e.g. if I pay the same amount ($d) for two items but incur a loss of x% on one of them but make a profit of y% for the other, we'll have to work it out. Only if x = y, this formula can be applied.

Let's say the x=y. Consider item 1. What's the CP? d/(1 - k) where k = x/100.
Similarly, for the other item, what's the CP? d/(1 + k).
Total CP = 2d/(1 - k*k)
Total SP = 2d.

Loss = 2d * (k^2)/(1 - k^2)

Loss percentage = Loss/Total CP = k^2. Substitute x back in the eqn. We have loss percentage = x^2/(100*100). This is a fraction mind you. To get a percent figure, multiply it by 100. So we've loss percentage = x^2/100 which is what we wanted.