# NIELIT 2019 Feb Scientist D - Section C: 28

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A two digit number is such that the product of the digits is $8$. When $18$ is added to the number, the digits are reversed. The number is :

1. $18$
2. $24$
3. $81$
4. $42$

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$24$

You can verify this question with the options also.

let tan’s digits =$x$

then unit digit=$\frac{8}{x}$

so the number is $10x+\frac{8}{x}$

now according to the question;

$\implies 10x+\frac{8}{x}+18=10*\frac{8}{x}+x$

$\implies \frac{10x^2+8+18x}{x}=\frac{80+x^2}{x}$

$\implies 9x^2+18x-72=0$

$\implies x^2+2x-8=0$

$\implies x(x+4)-2(x+4)=0$

$\implies(x+4)(x_2)=0$

$\implies x=-4,2$

$\therefore \text{tan’s digit=2, unit digit=$\frac{8}{2}$=4}$

So the number is $24$

Option $B$ is correct here.
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