Let's tackle the problem step by step.
### Step 1: Reading on the First Day
The boy reads [tex]\(\frac{1}{2}\)[/tex] of the book on the first day. This means half of the book is read on the first day.
### Step 2: Remaining Portion after the First Day
After the first day, since [tex]\(\frac{1}{2}\)[/tex] of the book is read, the remaining portion is:
[tex]\[ 1 - \frac{1}{2} = \frac{1}{2} \][/tex]
### Step 3: Reading on the Second Day
On the second day, the boy reads [tex]\(\frac{1}{2}\)[/tex] of the remaining portion. The remaining portion after the first day is [tex]\(\frac{1}{2}\)[/tex]. Hence, the boy reads:
[tex]\[ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \][/tex]
### Step 4: Total Portion Read in Two Days
Now, let's add the portions read on the first and second days to find out the total portion read in two days:
[tex]\[ \text{Portion read on the first day} + \text{Portion read on the second day} = \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \][/tex]
So, the boy reads [tex]\(\frac{3}{4}\)[/tex] of the book in two days.
### Step 5: Remaining Portion of the Book
The remaining portion of the book after two days is:
[tex]\[ 1 - \frac{3}{4} = \frac{1}{4} \][/tex]
### Step 6: Determine the Total Number of Pages
We know that 100 pages are left to be read, and this corresponds to [tex]\(\frac{1}{4}\)[/tex] of the book. To find the total number of pages in the book, we set up the equation:
[tex]\[ \frac{1}{4} \times \text{Total number of pages} = 100 \][/tex]
Solving for the total number of pages:
[tex]\[ \text{Total number of pages} = 100 \times 4 = 400 \][/tex]
### Summary
- The boy reads [tex]\(\frac{3}{4}\)[/tex] of the book in two days.
- The total number of pages in the book is 400.
