Question

There are \[160\] pages in a book. \[15\% \] of the pages have pictures on them. How many pages do not have pictures on them.

Answer 1

Hint: From the total number of pages, we can find the number of pages which have pictures using the percentage given. Then to find the number of pages which do not have a picture, we can simply subtract the number of pages with pages from the total number of pages.

Complete step-by-step answer:
The total number of pages in the book is \[160\].
Out of these \[15\% \] of them have pictures on them. To find the number of pages with pictures, we can use the formula of percentage to find it.
Let the number of pages with pictures be denoted by \[x\], so \[x\] is \[15\% \] of \[160\].
Writing this in the form of an equation, we get \[\dfrac{x}{{160}} = 15\% \].
This equation can be solved to give the value of \[x\], and thus the number of pages which have pictures on them.
\[
   \Rightarrow \dfrac{x}{{160}} = 15\% \\
   \Rightarrow \dfrac{x}{{160}} = \dfrac{{15}}{{100}} \\
   \Rightarrow x = \dfrac{{15 \times 160}}{{100}} \\
   \Rightarrow x = \dfrac{{15 \times 16}}{{10}} \\
   \Rightarrow x = \dfrac{{3 \times 16}}{2} \\
   \Rightarrow x = 3 \times 8 \\
   \Rightarrow x = 24 \\
\]
Thus, the total number of pages having pictures is \[24\].
So, the number of pages without pictures can be found out by subtracting the pages with pictures from total pictures.
Thus, the number of pages without pictures is \[160 - 24 = 136\] pages.

Note: The most common mistake that is done is while using the formula for percentage which should be avoided.
Another method of solving this question is finding the percentages of pages without pictures than using the formula for percentage to find the number of pages without pictures.
If the percentage of pages with pictures is \[15\% \] then the percentage of pages without pictures will \[100\% - 15\% = 85\% \].
Now, let us assume that the number of pages without pictures is \[y\]. That means \[y\] is \[85\% \] of \[160\].
We can find the exact number of pages without pictures by solving the percentage of formula for \[y\].
 \[
   \Rightarrow \dfrac{y}{{160}} = 85\% \\
   \Rightarrow \dfrac{y}{{160}} = \dfrac{{85}}{{100}} \\
   \Rightarrow y = \dfrac{{85 \times 160}}{{100}} \\
   \Rightarrow y = \dfrac{{85 \times 16}}{{10}} \\
   \Rightarrow y = \dfrac{{17 \times 16}}{2} \\
   \Rightarrow y = 17 \times 8 \\
   \Rightarrow y = 136 \\
\]
Thus, the number of pages without pictures comes out to be \[136\].