Mohit bought `5(1)/(2)` m of cloth for his kurta and `3(2)/(3)` m of cloth for his pyjamas. How much cloth did he purchase in all?

Options

A. `11(1)/(6)m`
B. `9(1)/(6)m`
C. `8(3)/(7)m`
D. `7(3)/(8)m`

Answer

To find out how much cloth Mohit purchased in total, we need to add the lengths of cloth he bought for his kurta and pyjamas. Here’s a step-by-step solution:

### Step 1: Write down the lengths of cloth purchased
Mohit bought:
- For his kurta: \( 5 \frac{1}{2} \) meters
- For his pyjamas: \( 3 \frac{2}{3} \) meters

### Step 2: Convert mixed fractions to improper fractions
To add these fractions, we first convert the mixed fractions into improper fractions.

1. For \( 5 \frac{1}{2} \):
- Multiply the whole number (5) by the denominator (2): \( 5 \times 2 = 10 \)
- Add the numerator (1): \( 10 + 1 = 11 \)
- So, \( 5 \frac{1}{2} = \frac{11}{2} \)

2. For \( 3 \frac{2}{3} \):
- Multiply the whole number (3) by the denominator (3): \( 3 \times 3 = 9 \)
- Add the numerator (2): \( 9 + 2 = 11 \)
- So, \( 3 \frac{2}{3} = \frac{11}{3} \)

### Step 3: Add the improper fractions
Now we need to add \( \frac{11}{2} \) and \( \frac{11}{3} \). To do this, we need a common denominator.

- The least common multiple (LCM) of 2 and 3 is 6.

Now, convert each fraction to have a denominator of 6:
1. For \( \frac{11}{2} \):
- Multiply the numerator and denominator by 3:
\[ \frac{11 \times 3}{2 \times 3} = \frac{33}{6} \]

2. For \( \frac{11}{3} \):
- Multiply the numerator and denominator by 2:
\[ \frac{11 \times 2}{3 \times 2} = \frac{22}{6} \]

### Step 4: Add the fractions
Now, we can add the two fractions:
\[ \frac{33}{6} + \frac{22}{6} = \frac{33 + 22}{6} = \frac{55}{6} \]

### Step 5: Convert the improper fraction back to a mixed number
To convert \( \frac{55}{6} \) back to a mixed number:
- Divide 55 by 6:
- 6 goes into 55 nine times (since \( 6 \times 9 = 54 \)).
- The remainder is \( 55 - 54 = 1 \).

Thus, \( \frac{55}{6} = 9 \frac{1}{6} \).

### Final Answer
Mohit purchased a total of \( 9 \frac{1}{6} \) meters of cloth.

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