Rohit bought a pencil for Rs `3(2)/(5)` and an eraser for Rs `2(7)/(10)` What is the total cost of both the articles?

Answer

To find the total cost of the pencil and eraser that Rohit bought, we will follow these steps:

### Step 1: Convert the mixed fractions to improper fractions.
1. **Cost of Pencil**:
- The cost of the pencil is given as \(3 \frac{2}{5}\).
- To convert this to an improper fraction:
\[ 3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \]

2. **Cost of Eraser**:
- The cost of the eraser is given as \(2 \frac{7}{10}\).
- To convert this to an improper fraction:
\[ 2 \frac{7}{10} = \frac{(2 \times 10) + 7}{10} = \frac{20 + 7}{10} = \frac{27}{10} \]

### Step 2: Add the two improper fractions.
To add \(\frac{17}{5}\) and \(\frac{27}{10}\), we need a common denominator. The least common multiple (LCM) of 5 and 10 is 10.

1. Convert \(\frac{17}{5}\) to have a denominator of 10:
\[ \frac{17}{5} = \frac{17 \times 2}{5 \times 2} = \frac{34}{10} \]

2. Now, add \(\frac{34}{10}\) and \(\frac{27}{10}\):
\[ \frac{34}{10} + \frac{27}{10} = \frac{34 + 27}{10} = \frac{61}{10} \]

### Step 3: Convert the improper fraction to a mixed number.
To convert \(\frac{61}{10}\) to a mixed number:
1. Divide 61 by 10:
- 10 goes into 61 six times (since \(10 \times 6 = 60\)).
- The remainder is \(61 - 60 = 1\).

Thus, we can write:
\[ \frac{61}{10} = 6 \frac{1}{10} \]

### Final Answer:
The total cost of both articles is \(6 \frac{1}{10}\) rupees.

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