160 cycles were sold for Rs. 524,000 resulting in a loss of 10% What was the cost price of a cycle (in Rs.)?(rounded off to the nearest rupee)

Options

A. 3275
B. 3639
C. 4321
D. 4763

Answer

To find the cost price of one cycle, we can follow these steps:

### Step 1: Understand the given information
We know that:
- Selling Price (SP) of 160 cycles = Rs. 524,000
- Loss = 10%

### Step 2: Calculate the Selling Price (SP) in terms of Cost Price (CP)
If there is a loss of 10%, the Selling Price is 90% of the Cost Price. We can express this relationship mathematically:
\[ SP = CP - (10\% \text{ of } CP) \]
This can be rewritten as:
\[ SP = 90\% \text{ of } CP \]
or
\[ SP = 0.9 \times CP \]

### Step 3: Set up the equation
Let the Cost Price (CP) of 160 cycles be represented as \( CP_{160} \).
Then, we can express the Selling Price in terms of Cost Price:
\[ 524,000 = 0.9 \times CP_{160} \]

### Step 4: Solve for Cost Price of 160 cycles
To find the Cost Price of 160 cycles, we rearrange the equation:
\[ CP_{160} = \frac{524,000}{0.9} \]
Calculating this gives:
\[ CP_{160} = \frac{524,000}{0.9} = 582,222.22 \]

### Step 5: Calculate the Cost Price of one cycle
To find the Cost Price of one cycle, we divide the total Cost Price by the number of cycles:
\[ CP_{1} = \frac{CP_{160}}{160} \]
\[ CP_{1} = \frac{582,222.22}{160} \]
Calculating this gives:
\[ CP_{1} = 3,638.89 \]

### Step 6: Round off to the nearest rupee
Rounding off 3,638.89 gives us:
\[ CP_{1} \approx 3,639 \]

### Final Answer
The cost price of one cycle is approximately Rs. 3,639.

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