The price of an article increase by 20% every year . If the difference between the price of the article at the end of the third year and at the end of the fourth year is ₹ 324, what is the price of the article at the end of the first year ? (a) ₹1,350 (b) ₹1,180 (c) ₹1,125 (d) ₹1,250?

Question

Answer

Given:
- The price of an article increases by 20% every year.
- The difference between the price of the article at the end of the third year and at the end of the fourth year is ₹ 324.

To find:
- The price of the article at the end of the first year.

Assumptions:
- Let the initial price of the article be P.

Solution:

Step 1: Understanding the price increase pattern
- The price of the article increases by 20% every year.
- Therefore, the price at the end of the first year would be P + 20% of P.
- Similarly, the price at the end of the second year would be (P + 20% of P) + 20% of (P + 20% of P).
- And so on.

Step 2: Calculating the price difference between the third and fourth year
- The price at the end of the third year = (P + 20% of P) + 20% of (P + 20% of P) + 20% of [(P + 20% of P) + 20% of (P + 20% of P)].
- The price at the end of the fourth year = (P + 20% of P) + 20% of (P + 20% of P) + 20% of [(P + 20% of P) + 20% of (P + 20% of P)] + 20% of [(P + 20% of P) + 20% of (P + 20% of P) + 20% of [(P + 20% of P) + 20% of (P + 20% of P)]].
- The difference between the price at the end of the third year and the fourth year is ₹ 324.
- Therefore, we have the equation: (Price at the end of the fourth year) - (Price at the end of the third year) = ₹ 324.

Step 3: Solving the equation to find the initial price (P)
- Substitute the expressions for the price at the end of the third and fourth year in the equation: (Price at the end of the fourth year) - (Price at the end of the third year) = ₹ 324.
- Simplify the equation and solve for P.

Step 4: Calculating the price at the end of the first year
- Use the value of P obtained in the previous step to calculate the price at the end of the first year: Price at the end of the first year = P + 20% of P.

Answer:
- The price of the article at the end of the first year is ₹1,125 (c).

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