A man sold his bicycle for Rs 810, losing one-tenth of its cost price, Find :
the loss

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define the Variables
Let the cost price (CP) of the bicycle be denoted as \( X \).

### Step 2: Calculate the Loss
According to the problem, the man loses one-tenth of the cost price. Therefore, the loss (L) can be expressed as:
\[ L = \frac{1}{10} \times X = \frac{X}{10} \]

### Step 3: Write the Selling Price Equation
We know that the selling price (SP) is given as Rs 810. The relationship between selling price, cost price, and loss is given by:
\[ SP = CP - L \]
Substituting the values we have:
\[ 810 = X - \frac{X}{10} \]

### Step 4: Simplify the Equation
To simplify the equation, we can rewrite \( X - \frac{X}{10} \) as:
\[ X - \frac{X}{10} = \frac{10X}{10} - \frac{X}{10} = \frac{9X}{10} \]
Thus, we can rewrite the equation as:
\[ 810 = \frac{9X}{10} \]

### Step 5: Solve for Cost Price
To find \( X \), we can multiply both sides of the equation by 10:
\[ 8100 = 9X \]
Now, divide both sides by 9:
\[ X = \frac{8100}{9} = 900 \]

### Step 6: Calculate the Loss
Now that we have the cost price, we can calculate the loss:
\[ L = \frac{X}{10} = \frac{900}{10} = 90 \]

### Final Answer
The loss incurred by the man is Rs 90.

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