Question

9. The radio of fiction books, non-fiction books and magazines in a school library is
3:5:2 Express this as a percentage the total number of books in the library is
10.000. find the numbers of books in each category.​

Answer 1

Correct Question :-

The ratio of fiction books, non-fiction books and magazines in a school library is 3:5:2. Express this as a percentage. The total number of books in the library is  10,000. Find the numbers of books in each category.​

SoluTion :-

Ratio = 3 : 5 : 2

Sum of ratio = 3 + 5 + 2 = 10

Now,

$\sf {Percentage \ of \ Fiction \ books = \dfrac{3}{10} \times 100=30 \%}\\\\\\\sf {Percentage \ of \ Non - Fiction \ books = \dfrac{5}{10} \times 100=50 \%}\\\\\\\sf {Percentage \ of \ Magazines = \dfrac{2}{10} \times 100=20 \%}$

No. of books = 10,000

Thus,

$\sf {No. \ of \ Fiction \ books = 30 \% \ of \ 10000}\\\\\\\sf {= \dfrac{30}{100} \times 10000=3000}\\\\\\\\\sf {No. \ of \ Non-Fiction \ books = 50 \% \ of \ 10000}\\\\\\\sf {= \dfrac{50}{100} \times 10000=5000}\\\\\\\\\sf {No. \ of \ Magazines = 20 \% \ of \ 10000}\\\\\\\sf {= \dfrac{20}{100} \times 10000=2000}$

AnswEr :-

Fiction books = 3000

Non-fiction books = 5000

Magazines = 2000

Answer 2

Answer:

Let the Fiction Books be 3n, Non - Fiction Books be 5n and Magazines be 2n.

⠀

$\Large\textit{1.}\:\sf Fiction\:Books :$

$:\implies\sf Fiction\:Books=\dfrac{Ratio}{Total\:Ratio} \times Total\:Books\\\\\\:\implies\sf Fiction\:Books = \dfrac{3n}{3n + 5n + 2n} \times 10000\\\\\\:\implies\sf Fiction\:Books = \dfrac{3n}{10n} \times 10000\\\\\\:\implies\sf Fiction\:Books = 3 \times 1000\\\\\\:\implies\sf Fiction\:Books = 3000$

$\rule{120}{0.8}$

$\dashrightarrow\sf\:\:Fiction\:Books\:\%=\dfrac{Fiction\:Books}{Total\:Books} \times 100\\\\\\\dashrightarrow\sf\:\:Fiction\:Books\:\% = \dfrac{3000}{10000} \times 100\\\\\\\dashrightarrow\sf\:\:Fiction\:Books\:\% = 30\%$

⠀⠀⠀$\rule{160}{1.5}$

$\Large\textit{2.}\:\sf Non-Fiction\:Books :$

$:\implies\sf Non-Fiction\:Books=\dfrac{Ratio}{Total\:Ratio} \times Total\:Books\\\\\\:\implies\sf Non-Fiction\:Books = \dfrac{5n}{3n + 5n + 2n} \times 10000\\\\\\:\implies\sf Non-Fiction\:Books = \dfrac{5n}{10n} \times 10000\\\\\\:\implies\sf Non-Fiction\:Books = 5\times 1000\\\\\\:\implies\sf Non-Fiction\:Books = 5000$

$\rule{120}{0.8}$

$\dashrightarrow\sf\:\:Non-Fiction\:Books\:\%=\dfrac{Non-Fiction\:Books}{Total\:Books} \times 100\\\\\\\dashrightarrow\sf\:\:Non-Fiction\:Books\:\% = \dfrac{5000}{10000} \times 100\\\\\\\dashrightarrow\sf\:\:Non-Fiction\:Books\:\% = 50\%$

⠀⠀⠀$\rule{160}{1.5}$

$\Large\textit{3.}\:\sf Magazines :$

$:\implies\sf Magazines=\dfrac{Ratio}{Total\:Ratio} \times Total\:Books\\\\\\:\implies\sf Magazines = \dfrac{2n}{3n + 5n + 2n} \times 10000\\\\\\:\implies\sf Magazines = \dfrac{2n}{10n} \times 10000\\\\\\:\implies\sf Magazines = 2\times 1000\\\\\\:\implies\sf Magazines = 2000$

$\rule{120}{0.8}$

$\dashrightarrow\sf\:\: Magazines\:\%=\dfrac{Magazines}{Total\:Books} \times 100\\\\\\\dashrightarrow\sf\:\:Magazines\:\% = \dfrac{2000}{10000} \times 100\\\\\\\dashrightarrow\sf\:\:Magazines\:\% = 20\%$