If the rate of a bed is increased by 17.89%, then by 13.43% and then by 8.93%, the price becomes Rs.2,765. What is the original price of the bed?
Question
If the rate of a bed is increased by 17.89%, then by 13.43% and then by 8.93%, the price becomes Rs.2,765. What is the original price of the bed?
Solution
1. ### Break Down the Problem
We need to find the original price of the bed before three successive percentage increases. Let the original price be denoted as .
2. ### Relevant Concepts
When a price increases successively by percentages, the new price can be calculated using the formula: where are the respective rate increases expressed as decimals.
3. ### Analysis and Detail
-
First percentage increase:
- New price after first increase:
-
Second percentage increase:
- New price after second increase:
-
Third percentage increase:
- New price after third increase:
Thus, we set up the equation:
-
Calculate the product of the multipliers:
- (approx)
- Then, (approx)
-
Substitute in the equation:
4. ### Verify and Summarize
Now, solving for :
Final Answer
The original price of the bed is approximately Rs. 1901.61.
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