math: alternative to profit/loss calculations ..

[mba_06]

I have stumbled upon an easier alternative to the successive gain/loss types of sums. Instead of doing calculations like 1.15 x 1.15 for a sum what involves successive profits of 15% you can try the following :

Question: Product P is marked up for a profit/loss of 15% and another profit/loss of 15% is made during a season sale etc..What
is the total profit on the product - instead of multiplying numbers like 1.15 x 1.15 (which can be painful if you are in a hurry,
you can follow this general observation that I have come up with while working on such calcuations one day!!

a. profit 15% + profit of 15% = add (15 +15) + (1.5 x 1.5) = 32.25 (total profile)
b. 15 profit + 15% loss = subtract loss from profit (15 -15) - (1.5 x 1.5) = -2.25 ( loss of 2.25)
c. 15% loss + 15 % profit = same as b.
d 15% loss + 15 % loss = 15 + 15 - (1.5x 1.5) = 27.75 ( total loss )


For the first part: Add/subtract the whole numbers beased on whether they are gain/loss.
a. gain, gain = gain + gain
b. gain, loss (and vise-versa) = gain - loss
c. loss, loss = loss + loss
Whenever there is a LOSS invloved always subtract the second part, (1.5 x 1.5), from the first part.
Also, the second part is derived by moving the decimal on the original numbers one place to the left.

I have found it to work with all numbers. It even can be used for compunt interest problems.

Disclaimer: I have not tested this against any mathematical principle. It works for me so thought I would share you you folks

Let me know your thoughs!

[arjmen]

Thanks for the post mba_06!!

General Case:

1) x% increase followed by a y% increase on a base amount of 'P'
Final amount = P(1+x)(1+y) ---> 'x' and 'y' in their decimal form
Initial amount = P

=> Change in Amount = P [1+x+y+xy] - P = P[(x+y)+(xy)]
=> Total percentage change = (x+y)+(xy)

2) x% increase followed by a y% decrease on a base amount of 'P'
Final amount = P(1+x)(1-y) ---> 'x' and 'y' in their decimal form
Initial amount = P

=> Change in Amount = P[1+x-y-xy] - P = P[(x-y)-(xy)]
=> Total percentage change = (x-y)-(xy)

3) x% decrease followed by y% decrease on a base amount of 'P'
Final amount = P(1-x)(1-y) ---> 'x' and 'y' in their decimal form
Initial amount = P
=> Change in Amount = P [1-x-y+xy] - P = P[-(x+y)+(xy)]
=> Total percentage change = -(x+y)+(xy)

[rum]

HI,

Could you please tell me how to solve this problem in the alternate methods mentioned above.

2. Mr. Adams sold 2 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 2 properties?
Loss of 1250
Loss of 2500
Gain of 1250
Gain of 2500
No gain, no loss

[mba_06]

HI,

Could you please tell me how to solve this problem in the alternate methods mentioned above.

2. Mr. Adams sold 2 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 2 properties?
Loss of 1250
Loss of 2500
Gain of 1250
Gain of 2500
No gain, no loss

Rum, I do not think the alternate method mentioned above applies to this case. In this case there are two different transactions taking place at two different costs/sale prices. The alternate method I had mentioned really applies to transaction done multiple times starting with one cost/sale price with successive profits/losses. That method basically substitutes difficult multiplications with easier additions/substractions.

hope that help!

good luck

[rayarya]

I have stumbled upon an easier alternative to the successive gain/loss types of sums. Instead of doing calculations like 1.15 x 1.15 for a sum what involves successive profits of 15% you can try the following :

Question: Product P is marked up for a profit/loss of 15% and another profit/loss of 15% is made during a season sale etc..What
is the total profit on the product - instead of multiplying numbers like 1.15 x 1.15 (which can be painful if you are in a hurry,
you can follow this general observation that I have come up with while working on such calcuations one day!!

a. profit 15% + profit of 15% = add (15 +15) + (1.5 x 1.5) = 32.25 (total profile)
b. 15 profit + 15% loss = subtract loss from profit (15 -15) - (1.5 x 1.5) = -2.25 ( loss of 2.25)
c. 15% loss + 15 % profit = same as b.
d 15% loss + 15 % loss = 15 + 15 - (1.5x 1.5) = 27.75 ( total loss )


For the first part: Add/subtract the whole numbers beased on whether they are gain/loss.
a. gain, gain = gain + gain
b. gain, loss (and vise-versa) = gain - loss
c. loss, loss = loss + loss
Whenever there is a LOSS invloved always subtract the second part, (1.5 x 1.5), from the first part.
Also, the second part is derived by moving the decimal on the original numbers one place to the left.

I have found it to work with all numbers. It even can be used for compunt interest problems.

Disclaimer: I have not tested this against any mathematical principle. It works for me so thought I would share you you folks

Let me know your thoughs!

I agree with this trick. Also, i wanted to point out based on your numbers that if you have to sqaure a number ending with 5, then this is the trick

lets say the number is: a5. Then (a5)^2 = a(a+1)25. Just place 25 next to a(a+1). ex: 45^2 = 4(4+1)25 ==> 2025

--C

[SangFroid]

Hey Mba, Arjmen and rayara,
why didn't u tell me this trick earlier ??
Thanks a lot for this.... really a genious beeline
by the way thanksa lot to Rum too...who sifted this from the old ones...
if he had not, then it would have remained hidden
This post really deserves a "Thumbs up"