Question

Sumit reads 2/9 of a book on Thursday, 1/3 on Friday and 1/6 on Saturday and remaining 100 pages on Sunday. How many pages are in the book?

Answer 1

Answer:

360 pages

Step-by-step explanation:

As per the provided information in the given question, we have :

• Pages are read by Sumit on Thursday = 2/9 of the book
• Pages are read by Sumit on Friday = 1/3 of the book
• Pages are read by Sumit on Saturday = 1/6 of the book
• Pages are read by Sumit on Sunday = 100

We are asked to calculate the number of pages in the book. Let us assume the number of the pages in the book as x.

― According to the question, Sumit reads 2/9 of a book on Thursday, 1/3 on Friday and 1/6 on Saturday and remaining 100 pages on Sunday. That means, pages are read by Sumit on Thursday is 2/9x , pages are read by him on Friday is 1/3x , pages are read by him on Saturday is 1/6x and pages are read by him on Sunday is 100 pages. The sum of all the pages read by him on each day will be equivalent to the total number of pages in the book.

Writing this statement in the form of a linear equation,

$\longrightarrow \sf{\quad { \dfrac{2}{9}x+ \dfrac{1}{3}x+ \dfrac{1}{6}x + 100 = x}}$

Taking the LCM in LHS and making the denominator equal in order to perform addition.

$\longrightarrow \sf{\quad { \dfrac{4x + 6x + 3x + 1800}{18} = x}}$

Now, performing addition of the like terms of the numerator of the fraction in LHS.

$\longrightarrow \sf{\quad { \dfrac{13x + 1800}{18} = x}}$

Transposing 18 from LHS to RHS. Its arithmetic operator will get changed.

$\longrightarrow \sf{\quad { 13x + 1800 =18x}}$

Transposing 13x from LHS to RHS, its sign will get changed.

$\longrightarrow \sf{\quad { 1800 =18x - 13x}}$

Performing subtraction in the RHS.

$\longrightarrow \sf{\quad { 1800 =5x}}$

Now, transposing 5 from RHS to LHS.Its arithmetic operator will get changed.

$\longrightarrow \sf{\quad { \cancel{\dfrac{1800}{5}} =x}}$

Dividing 1800 by 5.

$\longrightarrow \quad \underline{\boxed{ \textbf{\textsf{360 = x }}}}$

∴ The total number of pages in the book is 360 pages.