If the cost of 5 pencils is 3$\frac{3}{4}$ rupees then the cost of 2 pencils is

Question

Accepted Answer

To determine the cost of 2 pencils when the cost of 5 pencils is $3\frac{3}{4}$ rupees, we need to follow these steps:

1. **Convert Mixed Fraction to Improper Fraction:**
   The cost of 5 pencils is given as $3\frac{3}{4}$ rupees. First, convert this mixed fraction into an improper fraction:
   $$
   3\frac{3}{4} = \frac{15}{4}
   $$

2. **Find the Cost of One Pencil:**
   To find the cost of one pencil, divide the total cost by the number of pencils:
   $$
   \text{Cost of 1 pencil} = \frac{\frac{15}{4}}{5} = \frac{15}{4} \times \frac{1}{5} = \frac{15}{20} = \frac{3}{4} \text{ rupees}
   $$

3. **Calculate the Cost of 2 Pencils:**
   Multiply the cost of one pencil by 2 to find the cost of 2 pencils:
   $$
   \text{Cost of 2 pencils} = 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \text{ rupees}
   $$

Thus, the cost of 2 pencils is $\frac{3}{2}$ rupees, which corresponds to Option 2.

**Explanation of Why Other Options are Incorrect:**

1. **Option 1: Re. $\frac{3}{4}$**
   - This option suggests that the cost of 2 pencils is the same as the cost of 1 pencil, which is incorrect. The cost of 1 pencil is $\frac{3}{4}$ rupees, not 2 pencils.

2. **Option 3: Rs. $\frac{4}{3}$**
   - This option implies a cost calculation error. The correct calculation shows that the cost of 2 pencils is $\frac{3}{2}$ rupees, not $\frac{4}{3}$.

3. **Option 4: Re. $\frac{2}{3}$**
   - This option underestimates the cost of 2 pencils. The calculation clearly shows that the cost is $\frac{3}{2}$ rupees, not $\frac{2}{3}$.

In conclusion, the correct answer is Option 2, as the cost of 2 pencils is accurately calculated to be $\frac{3}{2}$ rupees.