A man buys 2 apples and 3 kiwi fruits for Rs 37. If he buys 4 apples and 5 kiwi fruits for Rs 67, then what will be the total cost of 1 apple and 1 kiwi fruit?

Options

A. Rs 15
B. Rs 28
C. Rs 18
D. Rs 20

Answer

To solve the problem step by step, we will set up equations based on the information provided.

### Step 1: Define Variables
Let:
- A = cost of 1 apple
- K = cost of 1 kiwi fruit

### Step 2: Set Up the Equations
From the problem statement, we have two scenarios:
1. 2 apples and 3 kiwi fruits cost Rs 37:
\[ 2A + 3K = 37 \quad \text{(Equation 1)} \]
2. 4 apples and 5 kiwi fruits cost Rs 67:
\[ 4A + 5K = 67 \quad \text{(Equation 2)} \]

### Step 3: Multiply Equation 1
To eliminate one of the variables, we can multiply Equation 1 by 2:
\[ 2(2A + 3K) = 2(37) \]
This gives us:
\[ 4A + 6K = 74 \quad \text{(Equation 3)} \]

### Step 4: Subtract Equation 2 from Equation 3
Now, we will subtract Equation 2 from Equation 3:
\[ (4A + 6K) - (4A + 5K) = 74 - 67 \]
This simplifies to:
\[ K = 7 \]

### Step 5: Substitute K back into Equation 1
Now that we have the value of K, we can substitute it back into Equation 1 to find A:
\[ 2A + 3(7) = 37 \]
This simplifies to:
\[ 2A + 21 = 37 \]
Subtracting 21 from both sides gives:
\[ 2A = 16 \]
Dividing by 2 results in:
\[ A = 8 \]

### Step 6: Find the Total Cost of 1 Apple and 1 Kiwi
Now we can find the total cost of 1 apple and 1 kiwi fruit:
\[ A + K = 8 + 7 = 15 \]

### Final Answer
The total cost of 1 apple and 1 kiwi fruit is Rs 15.

---