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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?

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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 P P .

2. ### Relevant Concepts

When a price increases successively by percentages, the new price can be calculated using the formula: New Price=P×(1+r1)×(1+r2)×(1+r3) \text{New Price} = P \times (1 + r_1) \times (1 + r_2) \times (1 + r_3) where r1,r2,r3 r_1, r_2, r_3 are the respective rate increases expressed as decimals.

3. ### Analysis and Detail

  1. First percentage increase:

    • r1=17.89%=0.1789 r_1 = 17.89\% = 0.1789
    • New price after first increase: P1=P×(1+0.1789)=P×1.1789 P_1 = P \times (1 + 0.1789) = P \times 1.1789
  2. Second percentage increase:

    • r2=13.43%=0.1343 r_2 = 13.43\% = 0.1343
    • New price after second increase: P2=P1×(1+0.1343)=P×1.1789×1.1343 P_2 = P_1 \times (1 + 0.1343) = P \times 1.1789 \times 1.1343
  3. Third percentage increase:

    • r3=8.93%=0.0893 r_3 = 8.93\% = 0.0893
    • New price after third increase: P3=P2×(1+0.0893)=P×1.1789×1.1343×1.0893 P_3 = P_2 \times (1 + 0.0893) = P \times 1.1789 \times 1.1343 \times 1.0893

Thus, we set up the equation: P×1.1789×1.1343×1.0893=2765 P \times 1.1789 \times 1.1343 \times 1.0893 = 2765

  1. Calculate the product of the multipliers:

    • 1.1789×1.13431.3397 1.1789 \times 1.1343 \approx 1.3397 (approx)
    • Then, 1.3397×1.08931.4570 1.3397 \times 1.0893 \approx 1.4570 (approx)
  2. Substitute in the equation: P×1.45702765 P \times 1.4570 \approx 2765

4. ### Verify and Summarize

Now, solving for P P : P27651.45701901.611 P \approx \frac{2765}{1.4570} \approx 1901.611

Final Answer

The original price of the bed is approximately Rs. 1901.61.

This problem has been solved

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