The cost of a pen is Rs `16 3/5` and that of a pencil is Rs `4 3/4` Which costs more and by how much

Answer

To solve the problem of comparing the costs of a pen and a pencil, we will follow these steps:

### Step 1: Convert the mixed fractions to improper fractions.
- The cost of the pen is given as Rs \(16 \frac{3}{5}\).
- To convert this to an improper fraction:
\[ 16 \frac{3}{5} = \frac{16 \times 5 + 3}{5} = \frac{80 + 3}{5} = \frac{83}{5} \]

- The cost of the pencil is given as Rs \(4 \frac{3}{4}\).
- To convert this to an improper fraction:
\[ 4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \]

### Step 2: Compare the two costs.
- Now we have:
- Cost of pen = \(\frac{83}{5}\)
- Cost of pencil = \(\frac{19}{4}\)

### Step 3: Find a common denominator to compare the fractions.
- The least common multiple (LCM) of the denominators 5 and 4 is 20.
- Convert both fractions to have a denominator of 20:
- For \(\frac{83}{5}\):
\[ \frac{83}{5} = \frac{83 \times 4}{5 \times 4} = \frac{332}{20} \]
- For \(\frac{19}{4}\):
\[ \frac{19}{4} = \frac{19 \times 5}{4 \times 5} = \frac{95}{20} \]

### Step 4: Subtract the costs to find the difference.
- Now, we can subtract the cost of the pencil from the cost of the pen:
\[ \frac{332}{20} - \frac{95}{20} = \frac{332 - 95}{20} = \frac{237}{20} \]

### Step 5: Convert the difference back to a mixed number.
- To convert \(\frac{237}{20}\) to a mixed number:
- Divide 237 by 20:
\[ 237 \div 20 = 11 \quad \text{(whole number)} \]
- Remainder:
\[ 237 - (20 \times 11) = 237 - 220 = 17 \]
- Therefore, \(\frac{237}{20} = 11 \frac{17}{20}\).

### Conclusion:
- The pen costs more than the pencil by Rs \(11 \frac{17}{20}\).

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