Vicky sold two bikes at the rate of Rs.327000 each. and he sold one bike at 40% profit, then find the profit obtained on the second bike if overall profit percentage of Vicky is 55.55%.

Let's solve this step by step:

### Given:
1. Vicky sold two bikes at Rs. 327,000 each.
2. One bike was sold at **40% profit**.
3. The **overall profit percentage** for both bikes combined is **55.55%**.

We need to determine the **profit obtained on the second bike**.

---

### Step 1: Let’s define the variables:
- **Cost price (CP)** of the first bike = \( CP_1 \)
- **Cost price (CP)** of the second bike = \( CP_2 \)

Since Vicky sells each bike for **Rs. 327,000**,  
- **Selling price (SP) of both bikes** = Rs. 327,000 each.

---

### Step 2: Profit on the first bike
The **profit percentage** on the first bike = 40%.  
Thus, the **cost price (CP)** of the first bike can be calculated as:

\[
SP_1 = CP_1 \times \left(1 + \frac{40}{100}\right)
\]

\[
327,000 = CP_1 \times 1.4
\]

\[
CP_1 = \frac{327,000}{1.4} = 233,571.43 \, \text{Rs.}
\]

The **profit on the first bike** is:

\[
\text{Profit on 1st bike} = 327,000 - 233,571.43 = 93,428.57 \, \text{Rs.}
\]

---

### Step 3: Calculate the overall profit
Since the **overall profit percentage** is 55.55%, the **total cost price (CP)** for both bikes is:

\[
\text{Total CP} = CP_1 + CP_2
\]

And the **total selling price (SP)** for both bikes is:

\[
\text{Total SP} = 327,000 + 327,000 = 654,000 \, \text{Rs.}
\]

Using the overall profit formula:

\[
\text{Overall profit} = \frac{(\text{Total SP} - \text{Total CP})}{\text{Total CP}} \times 100
\]

Given that the overall profit is **55.55%**:

\[
\frac{654,000 - (CP_1 + CP_2)}{CP_1 + CP_2} \times 100 = 55.55
\]

---

### Step 4: Expressing Total CP in terms of \(CP_2\)
Using \( CP_1 = 233,571.43 \):

\[
\frac{654,000 - (233,571.43 + CP_2)}{233,571.43 + CP_2} \times 100 = 55.55
\]

This simplifies to

Learn how to determine the profit on the second bike given an overall profit of 55.55% and individual bike selling prices. This problem involves calculating individual cost prices and overall profit percentage, suitable for Grades 8-10.

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