The cost of 6 gel pens and 16 ball pens is Rs. 92/-. What will be the cost of 27 gel pens and 72 ball pens?

Options

A. Rs. 440/-
B. Rs. 414
C. Rs. 430/-
D. Rs. 41 8/-

Answer

To solve the problem step by step, we will first find the cost of one gel pen and one ball pen based on the information given, and then use that to calculate the cost of 27 gel pens and 72 ball pens.

### Step 1: Set up the equation
Let the cost of one gel pen be \( G \) and the cost of one ball pen be \( B \). According to the problem, we have the equation:
\[ 6G + 16B = 92 \]

### Step 2: Simplify the equation
To simplify the equation, we can divide all terms by 2:
\[ 3G + 8B = 46 \]

### Step 3: Find the ratio of gel pens to ball pens
We need to find the cost of 27 gel pens and 72 ball pens. First, we can find the ratio of the number of gel pens to ball pens:
\[ \text{Ratio} = \frac{27}{72} \]
This simplifies to:
\[ \text{Ratio} = \frac{3}{8} \]

### Step 4: Scale the cost
Since the ratio of gel pens to ball pens in the original equation is also \( 3:8 \), we can multiply the total cost of \( 3G + 8B = 46 \) by 9 to find the cost for 27 gel pens and 72 ball pens:
\[ 9 \times (3G + 8B) = 9 \times 46 \]
Calculating this gives:
\[ 27G + 72B = 414 \]

### Step 5: Conclusion
Thus, the cost of 27 gel pens and 72 ball pens is Rs. 414.

### Final Answer:
The cost of 27 gel pens and 72 ball pens is Rs. 414.

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