Jonny has two cycles and one rickshaw. The rickshaw is worth Rs. 96. If he sells the rickshaw along with the first cycle, he has an amount double that of the value of the second cycle. But if he decides to sell the rickshaw along with the second cycle, the amount received would be less than the value of first cycle by Rs. 306. What is the value of first cycle?

Options

A. Rs. 900
B. Rs. 600
C. Rs. 498
D. None of these

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information given in the question.

### Step 1: Define Variables
Let:
- \( X \) = value of the first cycle
- \( Y \) = value of the second cycle
- The value of the rickshaw = Rs. 96

### Step 2: Set Up the First Equation
According to the problem, if Jonny sells the rickshaw along with the first cycle, he receives an amount that is double the value of the second cycle. This can be expressed as:
\[ 96 + X = 2Y \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
If Jonny sells the rickshaw along with the second cycle, he receives an amount that is Rs. 306 less than the value of the first cycle. This can be expressed as:
\[ 96 + Y = X - 306 \quad \text{(Equation 2)} \]

### Step 4: Rearrange Equation 2
We can rearrange Equation 2 to isolate \( Y \):
\[ Y = X - 306 - 96 \]
\[ Y = X - 402 \quad \text{(Equation 3)} \]

### Step 5: Substitute Equation 3 into Equation 1
Now, we will substitute Equation 3 into Equation 1:
\[ 96 + X = 2(X - 402) \]
Expanding the right side:
\[ 96 + X = 2X - 804 \]

### Step 6: Rearrange to Solve for X
Now, rearranging the equation to isolate \( X \):
\[ 96 + 804 = 2X - X \]
\[ 900 = X \]

### Step 7: Find the Value of Y
Now that we have \( X \), we can find \( Y \) using Equation 3:
\[ Y = 900 - 402 \]
\[ Y = 498 \]

### Conclusion
Thus, the value of the first cycle (X) is Rs. 900.