A bicycle passes through the hands of three dealers each of whom loses 5%. If the third buy it for Rs 6859, what did the first pay it?

Answer

To find out how much the first dealer paid for the bicycle, we can follow these steps:

### Step 1: Understand the Loss Percentage
Each dealer incurs a loss of 5%. This means that when a dealer sells the bicycle, they sell it for 95% of the price they paid.

### Step 2: Calculate the Selling Price of the Third Dealer
The third dealer bought the bicycle for Rs. 6859. This amount represents 90.25% of the first dealer's cost price (CP) because:
- The first dealer's CP is 100%.
- The second dealer sells it for 95% of the first dealer's CP.
- The third dealer sells it for 95% of the second dealer's selling price, which is 95% of 95% of the first dealer's CP.

Calculating 95% of 95%:
\[ 95\% \times 95\% = 0.95 \times 0.95 = 0.9025 = 90.25\% \]

### Step 3: Set Up the Equation
We know that 90.25% of the first dealer's CP equals Rs. 6859:
\[ 0.9025 \times \text{CP}_1 = 6859 \]

### Step 4: Solve for the First Dealer's Cost Price
To find the first dealer's CP, we rearrange the equation:
\[ \text{CP}_1 = \frac{6859}{0.9025} \]

### Step 5: Calculate the Value
Now, we perform the division:
\[ \text{CP}_1 = \frac{6859}{0.9025} \approx 7600 \]

### Conclusion
The first dealer paid approximately Rs. 7600 for the bicycle.

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