Rajesh reads 2 - 9 of a book on Friday- 1 - 3 of it on Saturday and the remaining 160 pages does the book have in all-

Total pages =x on Friday he reads ( 2/9)x pages on Saturday he reads (1/3)x =(3/9)x pages total pages he read is (2/9)x+(3/9)x=(5/9)x remaining pages = tota ...

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Standard XI

Mathematics

Properties of Set Operation

Rajesh reads ...

Question

Rajesh reads $\frac{2}{9}$ of a book on Friday, $\frac{1}{3}$ of it on Saturday and the remaining $160$ on Sunday. How many pages does the book have in all?

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Solution

Let Total pages $= x$
On Friday he reads $= \frac{2}{9} x$ pages
On Saturday he reads $= \frac{1}{3} x = \frac{3}{9} x$ pages [On multiplying $3$ in the numerator and denominator]

total pages he read on Friday and Saturday $= \frac{2}{9} x + \frac{3}{9} x = \frac{5}{9} x$

Remaining pages to read on Sunday $=$ total pages $-$ pages read on Friday and Saturday
$= x - \frac{5}{9} x$
$= \frac{4}{9} x$
The remaining pages to read on Sunday is given as $160$

$∴ \frac{4}{9} x = 160$
$\Rightarrow 4 x = 160 \times 9$
$\Rightarrow 4 x = 1440$
$\Rightarrow x = \frac{1440}{4} = 360$ pages
Hence, total pages $= 360$

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Rajesh reads $\frac{2}{9}$ of a book on Friday, $\frac{1}{3}$ of it on Saturday and the remaining $160$ on Sunday. How many pages does the book have in all?