Question

a boy reads 1/2pages of abook on day, on the next day, he reads 1/3 of remaining pages. how many pages does he reads in two days, if 100pages are left.how many page
s were in the book?​

Answer 1

$\bigstar$ Explanation $\bigstar$

$\leadsto$ Solution:-

Let the total number of pages be x

Number of pages read on the first day = x/2

Number of pages remaining = x - x/2 = x/2

Number of pages read on the second day = 1/3 $\times$ Number of pages remaining = 1/3 $\times$ x/2 = x/6

Number of pages remaining = x/2 - x/6 = x/3 [Here we have taken x/2 because already the boy had read x/2 pages and x/2 pages were remaining in the remaining x/2 the boy had read x/6]

But given that 100 pages were remaining unread'

Therefore,

x/3 = 100

x = 300

$\leadsto$ Concepts used in this question:-

i) Assuming a quantity as a variable

ii) Basic mathematical operations used in algebraic expressions

$\leadsto$ Formulas related to algebra:-

$\rm i) (a+b)^2 = a^2 + b^2 +2ab\\ii) (a-b)^2 = a^2 + b^2 - 2ab\\iii) (a+b)^3 = a^3 + b^3 + 3ab(a+b) \\iv) (a+b)^3 = a^3 - b^3 - 3ab(a-b)\\v)(a+b)(a-b) = a^2 - b^2\\vi) a^3 + b^3 = (a+b)(a^2 + b^2 - ab)\\vii) a^3 - b^3 = (a-b)(a^2 + b^2 + ab)$