Question

Hiee everyone..!!

Q : 1

In a library, 50 % of the total number of books is of Marathi. The books of English are 1/3 rd of Marathi books. The books on Mathematics are 25 % of the English books. The remaining 560 books are of other subjects. What is the total number of books in the library ?

Answer 1

$\textbf{SOLUTION :}$

Let the total number of books in the library be x

50% of these books is of Marathi.

» the number of Marathi books


$= \: 50\% \: of \: x \: = \: \frac{50}{100} \: \times \: x \: = \: \frac{x}{2}$


The books on English are  $\frac{1}{3}$ rd of Marathi books.


» the number of English books
$= \: \frac{x}{2} \times \frac{1}{3} = \frac{x}{6}$


The books on Mathematics are 25 % English books.


» the number of Mathematics books


$= 25\% \: of \: \frac{x}{6} \: = \: \frac{25}{100} \times \frac{x}{6} = \frac{x}{24}$


The remaining 560 books are of other subjects.


$x - ( \frac{x}{2} + \frac{x}{6} + \frac{x}{24}) \: = \textbf{560}$


Multiplying both sides by 24,


$24x - (12x + 4x + x) = 560 \times 24 \\ \\ > 24x - 17x = 560 \times 24 \\ \\ > 7x = 560 \times 24 \\ \\ > x = \frac{560 \times 24}{7} \\ \\ > x = 80 \times 24 \\ \\ > x = \textbf{1920}$


$\textbf{Ans :}$ The total number of books in library is $\textbf{1920}$.

Answer 2

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$\textbf{SOLUTION :}$

Let the total number of books in the library be x

50% of these books is of Marathi.

» the number of Marathi books

=$\: 50\% \: of \: x \: = \: \frac{50}{100} \: \times \: x \: = \: \frac{x}{2}$=50%ofx=

100

50

×x=

2

x

The books on English are \frac{1}{3}

3

1

rd of Marathi books.

» the number of English books

=$\: \frac{x}{2} \times \frac{1}{3}$ = \frac{x}{6}=

2

x

×

3

1

=

6

x

The books on Mathematics are 25 % English books.

» the number of Mathematics books

= 25\% \: of \: \frac{x}{6} \: = \: \frac{25}{100} \times \frac{x}{6} = \frac{x}{24}=25%of

6

x

=

100

25

×

6

x

=

24

x

The remaining 560 books are of other subjects.

x - ( \frac{x}{2} + \frac{x}{6} + \frac{x}{24}) \: = \textbf{560}x−(

2

x

+

6

x

+

24

x

)=560

Multiplying both sides by 24,

$\begin{lgathered}$24x - (12x + 4x + x) = 560 \times 24 \\ \\ > 24x - 17x = 560 \times 24 \\ \\ > 7x = 560 \times 24 \\ \\ > x =$\frac{560 \times 24}{7}$ \\ \\ > x = 80 \times 24 \\ \\ > x = $\textbf{1920}\end{lgathered}$

24x−(12x+4x+x)=560×24

>24x−17x=560×24

>7x=560×24

>x=

7

560×24

>x=80×24

>x=1920