Find the ratio of the price of a pencil to that of a ball pen if pencils cost ₹ 96 per score and ball pens cost ₹ 50.40 per dozen.

Answer

To find the ratio of the price of a pencil to that of a ball pen, we will follow these steps:

### Step 1: Understand the given prices
- The cost of pencils is ₹96 per score.
- The cost of ball pens is ₹50.40 per dozen.

### Step 2: Convert 'score' and 'dozen' to actual quantities
- A score is equal to 20. Therefore, 1 score of pencils means 20 pencils.
- A dozen is equal to 12. Therefore, 1 dozen of ball pens means 12 ball pens.

### Step 3: Calculate the cost of one pencil
To find the cost of one pencil, we divide the total cost of the score of pencils by the number of pencils in a score:
\[ \text{Cost of one pencil} = \frac{96}{20} = 4.8 \text{ rupees} \]

### Step 4: Calculate the cost of one ball pen
To find the cost of one ball pen, we divide the total cost of the dozen ball pens by the number of ball pens in a dozen:
\[ \text{Cost of one ball pen} = \frac{50.40}{12} = 4.20 \text{ rupees} \]

### Step 5: Find the ratio of the price of a pencil to that of a ball pen
Now, we can find the ratio of the price of one pencil to the price of one ball pen:
\[ \text{Ratio} = \frac{\text{Cost of one pencil}}{\text{Cost of one ball pen}} = \frac{4.8}{4.20} \]

### Step 6: Simplify the ratio
To simplify the ratio, we can multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ \frac{4.8 \times 10}{4.20 \times 10} = \frac{48}{42} \]
Now, we simplify \( \frac{48}{42} \):
\[ \frac{48 \div 6}{42 \div 6} = \frac{8}{7} \]

### Final Answer
The ratio of the price of a pencil to that of a ball pen is:
\[ \text{Ratio} = 8 : 7 \]

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