5 cans of lemon drink and 7 packets of litchi juice cost Rs. 50 while 7 cans of lemon drink and 5 packets of litchi juice cost Rs. 46. Calculate the cost of one can of lemon drink.

Options

A. Rs. 8
B. Rs. 12
C. Rs. 3
D. Rs. 5

Answer

To solve the problem step by step, we will set up a system of equations based on the information given in the question.

### Step 1: Define Variables
Let:
- \( x \) = cost of one can of lemon drink (in Rs)
- \( y \) = cost of one packet of litchi juice (in Rs)

### Step 2: Set Up the Equations
From the problem, we have two pieces of information that we can translate into equations:

1. The cost of 5 cans of lemon drink and 7 packets of litchi juice is Rs. 50:
\[ 5x + 7y = 50 \quad \text{(Equation 1)} \]

2. The cost of 7 cans of lemon drink and 5 packets of litchi juice is Rs. 46:
\[ 7x + 5y = 46 \quad \text{(Equation 2)} \]

### Step 3: Solve the System of Equations
We will use the elimination method to solve these equations.

**Multiply Equation 1 by 5:**
\[ 5(5x + 7y) = 5(50) \implies 25x + 35y = 250 \quad \text{(Equation 3)} \]

**Multiply Equation 2 by 7:**
\[ 7(7x + 5y) = 7(46) \implies 49x + 35y = 322 \quad \text{(Equation 4)} \]

### Step 4: Subtract Equation 3 from Equation 4
Now, we subtract Equation 3 from Equation 4 to eliminate \( y \):
\[ (49x + 35y) - (25x + 35y) = 322 - 250 \]
This simplifies to:
\[ 24x = 72 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 24:
\[ x = \frac{72}{24} = 3 \]

### Step 6: Find the Value of \( y \) (Optional)
To find \( y \), we can substitute \( x = 3 \) back into either Equation 1 or Equation 2. Let's use Equation 1:
\[ 5(3) + 7y = 50 \]
This simplifies to:
\[ 15 + 7y = 50 \]
Subtract 15 from both sides:
\[ 7y = 35 \]
Now divide by 7:
\[ y = 5 \]

### Final Answer
The cost of one can of lemon drink is Rs. 3.

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