64
Math Steps 5
½
14. A boy reads of a book on the first day. On the second day he reads of the remaining
portion. What portion of the book does the boy
read in the
two days? If 100 pages are left
to be read, find how many pages are there in the book.



Answer :

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.