Puzzle Master  New Month  New Puzzle  Jewel Puzzle
A jewellery shop owner conducts his business in the following manner.
Every once in a while he raises his prices by the same percentage. After one such up down cycle of increasing and then decreasing his price by x% the price of a jewel decreases by rs100. In the next cycle he increases and decreases his price by (x/2% and then sells the jewel for rs2346. What is the initial price of the jewel (in rs) .... ?
Every once in a while he raises his prices by the same percentage. After one such up down cycle of increasing and then decreasing his price by x% the price of a jewel decreases by rs100. In the next cycle he increases and decreases his price by (x/2% and then sells the jewel for rs2346. What is the initial price of the jewel (in rs) .... ?
Replies

Sagar07m getting some fractional errors..... will that do??????

Radhika DeshpandeTry it. It wont give you any fractional error.

Sagar07ok, i will try to solve it...................

Radhika DeshpandeNo other takers ?
Should I post the answer ?ðŸ˜• 
Ramani Aswath
The problem as stated has an answer. However it is not simple.FrootyNo other takers ? Should I post the answer ?ðŸ˜•
Let P be the initial price. For interest rate r = x/100, (working with a fraction is easier than using % as you avoid dividing by 100. There is no difference to the calculations),
P  P(1+r)(1r) =100
Solving for r,
r = 10/sqrt(P)........(1)
For interest rate r/2,
(P 100)(1 + r/2 )(1r/2) = 2346 (given)
Substituting for r from (1), collecting like terms and simplifying we get a quadratic,
P[SUP]2[/SUP]  2471P + 2500 = 0
Solving the quadratic we get,
P = 2470 (rounded of to the nearest rupee).
r=.2012 (rounded to the 4th place)
x = 20.12%
P(1  x[SUP]2[/SUP]) = 2370 (rounded off value) This is INR 100 less than the initial price, which is given.
The solution is self consistent and so correct.
I think that there must be some error in the problem statement.
On the other hand, if the price after the second round of x/2 rate is 2376 instead of 2346 (which is given), then the answer is really simple.
The initial price then becomes INR 2500, x = 20%,the price after first round becomes INR 2400 (which matches the INR 100 specified) and the final price after x/2 (10%) raising and lowering is INR 2376. 
Sagar07Initial price=2470rs.... x=20.12%..... then after first cycle of increasing and decreasing by x%... price=2470*(1.2012)*(0.7988)=2370 rs............
after second cycle of increasing and decreasing by x/2%..... price=2370*(1.1006)*(0.8994)=2346 rs.............. 
Radhika DeshpandeSorry for not posting the answer ..
Well from the given condition what i have is that the answer goes like this 
2346/2 = 1173
1173  100 = 1073 
Ramani AswathThe initial price has to be always more than the final price if the cycle involves initially raising by x% and then decreasing by the same x%.
For each cycle if the initial price is P and the % is x then the final price = P(10000  x[SUP]2[/SUP])/10000.
Then the answer given by the other two posters has to be correct.
1073 does not match the stated conditions, unless we misread the boundary conditions and the statement means something else.
I shall be very much interested in knowing the detailed working behind the given answer. 
Sagar07even i didn't get the answer given by frooty.... will u plz elaborate?????

Radhika DeshpandeYes you both are correct .. Even I am thinking there is some mistakes in given conditions. .. I will recheck it and post the answer as soon as I get it .

Ramani Aswath
The simplest explanation is tht there is a typo in the condition of the second cycle value of 2346. It is possible that instead of 7, 4 was typed in. 4 minus the horizontal stroke looks a lot like 7.FrootyYes you both are correct .. Even I am thinking there is some mistakes in given conditions. .. I will recheck it and post the answer as soon as I get it .
If the second value is indeed 2376 we do get a simple, elegant and satisfying solution.
You are reading an archived discussion.
Related Posts
Narayana Murthy, founder of Indian IT major Infosys said that the quality of students entering IIT is declining because of mushrooming coaching classes that prepare students for IIT exams. Murthy...
12
123
1234
12345
23
234
2345
34
345
3456
45
456
56
Please help me thanks a lot
f u are thinking of buying tikona broadband
never buy it !!
i am using tikona broadband for last 2 month to get high speed but i did not get...
Attending Oracle OpenWorld is the most costeffective and efficient way to stay ahead of the technology curveâ€”and this year's event incorporates the popular Oracle Develop event as an official Oracle...
Yesterday i get chance to meet CeanPatty for 1015 Minutes and today I Spent a Super Day with Mayur Pathak.
It was amazing !!