Transaction Loss/Gain

shankar.ashwin wrote:Steve purchased ‘a’ pencils for ‘b’ dollars. Lisa purchased ‘b’ erasers for ‘a’ dollars. Steve exchanges one pencil for an eraser with Lisa. Find the percentage gain or loss of Steve on the exhange if a>b?

(A) (a^2 - b^2)/b^2 * 100% gain
(B) (a^2 - b^2)/b^2 * 100% loss
(C) (a^2 - b^2)/a^2 * 100% gain
(D) (a^2 - b^2)/a^2 * 100% loss
(E) (a^2 - b^2)/2ab * 100% gain

Plugin in some arbitrary values of a and b satisfying the condition a>b

Let a = 4 and b = 2


So the question looks like -

Steve purchased 4 pencils for 2 dollars. Lisa purchased 2 erasers for 4 dollars. Steve exchanges one pencil for an eraser with Lisa.


Now cost of 1 pencil is $0.50 {Steve}

Cost of 1 eraser is $2.00 { Lisa}


Steve exchanges one pencil for an eraser with Lisa.

So Steve got an eraser of $2.00 in return by spending $0.50

Hence he made a profit of $1.50...

Now the profit % he made is -


(1.50/0.50)*100 =>300% ....



NOW GO THRU THE OPTIONS -

We can straightaway reject options B and D because the tells us about a loss...




let's proceed further ....

We find that (a^2 - b^2) is common to option A , C and E...


Plugging in the values of a as 4 and b as 2 we get-


(a^2 - b^2) = > 16 - 4 = 12

b^2 = 2^2 =>4

So,(a^2 - b^2)/b^2 => 12/4 *1005 =300% profit ....


So , The correct answer is option A...

shankar.ashwin wrote:Steve purchased ‘a’ pencils for ‘b’ dollars. Lisa purchased ‘b’ erasers for ‘a’ dollars. Steve exchanges one pencil for an eraser with Lisa. Find the percentage gain or loss of Steve on the exhange if a>b?

(A) (a^2 - b^2)/b^2 * 100% gain
(B) (a^2 - b^2)/b^2 * 100% loss
(C) (a^2 - b^2)/a^2 * 100% gain
(D) (a^2 - b^2)/a^2 * 100% loss
(E) (a^2 - b^2)/2ab * 100% gain

price of each pencil for Steve = b/a
price of each eraser for Lisa = a/b

given that Steve has exchanged an pencil for an eraser.
As a>b, clearly steve made profit.

For this transaction (exchange) the profit % can be calculated as
(difference between costs of eraser and pencil)/cost price of pencil*100%
= ((a/b)-(b/a))/b/a*100%
= ([a^2]/[b^2])-1 *100%
= (a^2-b^2)/b^2 * 100% gain

so the answer is A

what is the OA??

Regards,
Chetan