A shopkeeper sells a pencil for Rs. `5 (1)/(4)`. He makes a total of Rs. `446 (1)/(4)` by the end of the day. If the pencils came in boxes of 15 each, how many boxes has he sold by the end of the day?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Convert mixed fractions to improper fractions
The price of one pencil is given as Rs. \(5 \frac{1}{4}\) and the total earnings are Rs. \(446 \frac{1}{4}\).

1. Convert \(5 \frac{1}{4}\) to an improper fraction:
\[ 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \]

2. Convert \(446 \frac{1}{4}\) to an improper fraction:
\[ 446 \frac{1}{4} = \frac{446 \times 4 + 1}{4} = \frac{1784 + 1}{4} = \frac{1785}{4} \]

### Step 2: Calculate the number of pencils sold
Now, we need to find out how many pencils were sold by dividing the total earnings by the price of one pencil.

\[ \text{Number of pencils sold} = \frac{\text{Total earnings}}{\text{Price per pencil}} = \frac{\frac{1785}{4}}{\frac{21}{4}} \]

### Step 3: Simplify the division of fractions
To divide by a fraction, we multiply by its reciprocal:

\[ \frac{\frac{1785}{4}}{\frac{21}{4}} = \frac{1785}{4} \times \frac{4}{21} = \frac{1785}{21} \]

### Step 4: Perform the division
Now, we calculate \(1785 \div 21\):

1. Perform the division:
\[ 1785 \div 21 = 85 \]

So, the number of pencils sold is 85.

### Step 5: Calculate the number of boxes sold
Since each box contains 15 pencils, we need to divide the total number of pencils sold by the number of pencils per box:

\[ \text{Number of boxes sold} = \frac{85}{15} \]

### Step 6: Simplify the division
Now, we perform the division:

1. Calculate \(85 \div 15\):
\[ 85 \div 15 = 5 \quad \text{(with a remainder of 10)} \]

This means he sold 5 full boxes and has 10 pencils left over.

### Final Answer
The shopkeeper sold **5 boxes** of pencils.

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