The cost of a pen is Rs `16(2)/(3)` and that of a pencil is Rs `4(1)/(6)` Which costs more ?

Options

A. Pen
B. Pencil
C. Can not be determined
D. None of these

Answer

To determine which item costs more between a pen and a pencil, we need to convert the mixed fractions into improper fractions and then compare them.

### Step 1: Convert the cost of the pen into an improper fraction.
The cost of the pen is given as Rs \( 16 \frac{2}{3} \).

To convert this mixed number into an improper fraction:
1. Multiply the whole number (16) by the denominator (3):
\( 16 \times 3 = 48 \).
2. Add the numerator (2) to this product:
\( 48 + 2 = 50 \).
3. Place this result over the original denominator (3):
\[ \text{Cost of pen} = \frac{50}{3} \]

### Step 2: Convert the cost of the pencil into an improper fraction.
The cost of the pencil is given as Rs \( 4 \frac{1}{6} \).

To convert this mixed number into an improper fraction:
1. Multiply the whole number (4) by the denominator (6):
\( 4 \times 6 = 24 \).
2. Add the numerator (1) to this product:
\( 24 + 1 = 25 \).
3. Place this result over the original denominator (6):
\[ \text{Cost of pencil} = \frac{25}{6} \]

### Step 3: Compare the two costs.
Now we need to compare \( \frac{50}{3} \) and \( \frac{25}{6} \). To do this, we can find a common denominator.

The least common multiple (LCM) of 3 and 6 is 6.

1. Convert \( \frac{50}{3} \) to a fraction with a denominator of 6:
\[ \frac{50}{3} \times \frac{2}{2} = \frac{100}{6} \]

2. Now we can compare \( \frac{100}{6} \) and \( \frac{25}{6} \):
- Since \( 100 > 25 \), it follows that \( \frac{100}{6} > \frac{25}{6} \).

### Conclusion:
The cost of the pen (Rs \( 16 \frac{2}{3} \) or \( \frac{100}{6} \)) is greater than the cost of the pencil (Rs \( 4 \frac{1}{6} \) or \( \frac{25}{6} \)).

### Step 4: Calculate the difference in cost.
To find out how much more the pen costs than the pencil:
\[ \text{Difference} = \frac{100}{6} - \frac{25}{6} = \frac{100 - 25}{6} = \frac{75}{6} = 12 \frac{1}{2} \]

### Final Answer:
The pen costs more than the pencil by Rs \( 12 \frac{1}{2} \).

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