Frooty

No other takers ? Should I post the answer ?😕

The problem as stated has an answer. However it is not simple.

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)(1-r) =100

Solving for r,

r = 10/sqrt(P)........(1)

For interest rate r/2,

(P -100)(1 + r/2 )(1-r/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.