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We have 1.5 mins....Lets go! The owner of an art shop

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We have 1.5 mins....Lets go! The owner of an art shop [#permalink] New post 14 Sep 2003, 03:59
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We have 1.5 mins....Lets go!

The owner of an art shop conducts his business in the following
manner: Every once in a while he raises his prices by X%, then a while
later he reduces all the new prices by X%. After one such up-down cycle,
the price of a painting decreased by Rs 441. After a second up-down cycle
the painting was sold for Rs 1944.81. What was the original price of the
painting?

a) 2756.25
b) 2256.25
c) 2500
d) 2000

explain at leisure!

thanks
praetorian
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 [#permalink] New post 16 Sep 2003, 21:22
I tried and couldn't find a solution! I'm desperate to see how this is cracked!
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Get with the program!

CEO
CEO
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Joined: 15 Aug 2003
Posts: 3470
Followers: 60

Kudos [?]: 670 [0], given: 781

 [#permalink] New post 16 Sep 2003, 22:54
lazerbud wrote:
I tried and couldn't find a solution! I'm desperate to see how this is cracked!



The "441" solves 99% of the problem in 30 seconds....but just to give you a explanation..here goes


1st equation
Let SP be original selling price
SP*(1+ X/100) (1-X/100) = SP-441

2nd Equation
(SP-441) * (1+X/100)(1-X/100) = 1944.81 .....eqn 2

Now, from 1... (1+ X/100) (1-X/100) = SP-441 /SP

Therefore

(SP -441) * (SP-441) /SP[b]= 1944.81 .....equation 3

[b]Some Common Sense

Look at the answer choices...it cant be 2000 and 2256..because the first "round" itself reduces the price by 441 which will be less than 1944.81...so these two are incorrect.
Also 2500 gets reduced to 2059 in the first "round ".....its too close to 1944.81 in the first round itself...but just to be sure..

We'll try the largest value 2756.25 ..Lets approximate SP to 2800
and 441 to 500 ...cool? ok

(2800-500)*(2800-500) /2800 = 2300 *23/28 =52900/28 => 1889
Thats as close as you can get in 45 seconds..

Answer A

comments?
thanks
praetorian
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Joined: 28 Aug 2003
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Location: USA
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 [#permalink] New post 18 Sep 2003, 16:03
praetorian123 wrote:
lazerbud wrote:
I tried and couldn't find a solution! I'm desperate to see how this is cracked!



The "441" solves 99% of the problem in 30 seconds....but just to give you a explanation..here goes


1st equation
Let SP be original selling price
SP*(1+ X/100) (1-X/100) = SP-441

2nd Equation
(SP-441) * (1+X/100)(1-X/100) = 1944.81 .....eqn 2

Now, from 1... (1+ X/100) (1-X/100) = SP-441 /SP

Therefore

(SP -441) * (SP-441) /SP[b]= 1944.81 .....equation 3

[b]Some Common Sense

Look at the answer choices...it cant be 2000 and 2256..because the first "round" itself reduces the price by 441 which will be less than 1944.81...so these two are incorrect.
Also 2500 gets reduced to 2059 in the first "round ".....its too close to 1944.81 in the first round itself...but just to be sure..

We'll try the largest value 2756.25 ..Lets approximate SP to 2800
and 441 to 500 ...cool? ok

(2800-500)*(2800-500) /2800 = 2300 *23/28 =52900/28 => 1889
Thats as close as you can get in 45 seconds..

Answer A

comments?
thanks
praetorian


Good explanation Praet! Man, you are fast. I took several minutes to partially solve the problem.
  [#permalink] 18 Sep 2003, 16:03
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We have 1.5 mins....Lets go! The owner of an art shop

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