If John sells his bicycle for Rs 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5%?

Answer

To solve the problem step by step, we will first find the cost price (CP) of the bicycle using the given selling price (SP) and the loss percentage. Then, we will calculate the selling price required for a desired profit percentage.

### Step 1: Identify the given values
- Selling Price (SP) = Rs 637
- Loss Percentage = 9%

### Step 2: Calculate the Cost Price (CP)
To find the Cost Price when the Selling Price and Loss Percentage are given, we use the formula:

\[ CP = \frac{100}{100 - \text{Loss Percentage}} \times SP \]

Substituting the values:

\[ CP = \frac{100}{100 - 9} \times 637 \]

\[ CP = \frac{100}{91} \times 637 \]

Now, calculating the value:

\[ CP = \frac{100 \times 637}{91} = \frac{63700}{91} \approx 700 \]

So, the Cost Price (CP) is Rs 700.

### Step 3: Calculate the Selling Price for a Profit of 5%
Now, we need to find the Selling Price (SP) when John wants to make a profit of 5%. We use the formula:

\[ SP = \left( \frac{100 + \text{Profit Percentage}}{100} \right) \times CP \]

Substituting the values:

\[ SP = \left( \frac{100 + 5}{100} \right) \times 700 \]

\[ SP = \left( \frac{105}{100} \right) \times 700 \]

Calculating the value:

\[ SP = 1.05 \times 700 = 735 \]

So, the Selling Price (SP) for a profit of 5% should be Rs 735.

### Final Answer:
John should sell the bicycle for Rs 735 to achieve a profit of 5%.

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