44
A 2-digit number is seven times the sum of its digits and two (2) more than 5 times the product of its digits. Find the number.
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Let digit at unit place be $x$ and digit at tens place be $y$
$\therefore$ number $= 10y + x$
$ATQ$
$10y + x = 7(x + y)$
$\implies 3y = 6x$ or $y = 2x$ --- (1)
Also, $10y + x = 5xy + 2$ --- (2)
from (1) and (2), we get $10x^2 - 21x + 2 = 0$
$\implies (x - 2)(10x - 1) = 0$
$\therefore x = 2$
So, $y = 4$
$\therefore$ Required number is 42.
$\therefore$ number $= 10y + x$
$ATQ$
$10y + x = 7(x + y)$
$\implies 3y = 6x$ or $y = 2x$ --- (1)
Also, $10y + x = 5xy + 2$ --- (2)
from (1) and (2), we get $10x^2 - 21x + 2 = 0$
$\implies (x - 2)(10x - 1) = 0$
$\therefore x = 2$
So, $y = 4$
$\therefore$ Required number is 42.