Lalit reads a book for `1 3/4` hours every day and reads the entire book in 6 days. How many hours does he take to read the entire book?

Options

A. `10 1/2`hours
B. `9 1/2`hours
C. `7 1/2`hours
D. `11 1/2`hours

Answer

To find out how many hours Lalit takes to read the entire book, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
Lalit reads for \(1 \frac{3}{4}\) hours each day. We first convert this mixed number to an improper fraction.

\[ 1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \text{ hours} \]

### Step 2: Calculate the total hours read in 6 days
Now that we know Lalit reads \(\frac{7}{4}\) hours each day, we can find out how many hours he reads in 6 days by multiplying the daily reading time by the number of days.

\[ \text{Total hours} = \text{Daily hours} \times \text{Number of days} = \frac{7}{4} \times 6 \]

### Step 3: Perform the multiplication
To multiply \(\frac{7}{4}\) by 6, we can write 6 as a fraction:

\[ \frac{7}{4} \times 6 = \frac{7}{4} \times \frac{6}{1} = \frac{7 \times 6}{4 \times 1} = \frac{42}{4} \]

### Step 4: Simplify the fraction
Now, we simplify \(\frac{42}{4}\):

\[ \frac{42}{4} = \frac{21}{2} \text{ hours} \]

### Step 5: Convert to mixed number
Finally, we can convert \(\frac{21}{2}\) to a mixed number:

\[ \frac{21}{2} = 10 \frac{1}{2} \text{ hours} \]

### Conclusion
Thus, Lalit takes **10 hours and 30 minutes** (or \(10 \frac{1}{2}\) hours) to read the entire book.

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