at the beginning of the year, the owner of a jewel shop raised the prices of all the jewel in his shop by x% and lowered then by x%. The price of one jewel after this up and down cycle reduced by rs 100. the owner carried out the same procedure after a month. after this second up down cycle the price of that jewel was rs 2304. find the original price of that jewel.?

Question

at the beginning of the year, the owner of a jewel shop raised the prices of all the jewel in his shop by x% and lowered then by x%. The price of one jewel after this up and down cycle reduced by rs 100. the owner carried out the same procedure after a month. after this second up down cycle the price of that jewel was rs 2304. find the original price of that jewel.?

But i have seen solutions which posted by your faculty but i didn't understand can you do in simplified way please help

Answer 1

Sure, I can explain the problem and solution in a simplified way.

Let's assume the original price of the jewel is P.

According to the given information, the owner raised the price by x% and then lowered it by x%. This means that the price was increased by x% and then decreased by x% of the increased price.

When the price was increased by x%, the new price of the jewel became P + (P * x/100).

Next, when the price was decreased by x% of the increased price, the new price became (P + (P * x/100)) - ((P + (P * x/100)) * x/100).

According to the problem, after this up and down cycle, the price reduced by Rs 100. So, we can write the equation:

(P + (P * x/100)) - ((P + (P * x/100)) * x/100) = P - 100

Now, we can simplify and solve this equation to find the value of P.

Let's solve this step by step:

Step 1: Simplify the equation

P + (P * x/100) - (P + (P * x/100)) * x/100 = P - 100

Step 2: Distribute the terms

P + P * x/100 - P * x/100 - (P * x/100) * x/100 = P - 100

Step 3: Combine like terms

P - P * x^2/10000 = P - 100

Step 4: Cancel out P terms

- P * x^2/10000 = - 100

Step 5: Multiply both sides by -10000

P * x^2 = 100 * 10000

Step 6: Divide both sides by x^2

P = (100 * 10000) / x^2

Now we have the original price P in terms of x.

Next, we are given that the owner carried out the same procedure after a month and the price became Rs 2304.

Applying the same equation for the second cycle:

(P + (P * x/100)) - ((P + (P * x/100)) * x/100) = 2304 - P

Simplifying and solving this equation will give us the value of x.

Once we have the value of x, we can substitute it back into the equation to find the original price P.