Two numbers differ by 40.
Question:

Two numbers differ by 40. When each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the

other number is (40 – x).

Solution:

False

Given, one number $=x$

and other number $=40-x$

Let $(40-x)>x$

Then, according to the question,

$40-x+8=3(x+8)$

$\Rightarrow \quad 48-x=3 x+24$

$\Rightarrow \quad-x-3 x=24-48 \quad$ [transposing $3 x$ to LHS and 48 to RHS]

$\Rightarrow$ $-4 x=-24$

$\Rightarrow$ $x=-24 \times\left(-\frac{1}{4}\right)$

$\therefore$ $x=6$

Hence, one number $=x=6$

and other number $=40-x=40-6=34$

Now, difference between numbers $=34-6=28 \neq 40$ which is not satisfy the condition given in question.

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