Question

A two digit number is 3 more than 4 times the sum of digits.it 18 is added to this number the sum is equal to the number obtained by interchanging the digits.find the number

Answer 1

Let $10y+x$ be two digit number.

Given: $10y+x=4(y+x)+3$

$\Rightarrow 10y+x=4y+4x+3$

$\Rightarrow 6y=3x+3$.

$\Rightarrow 2y=x+1$

$\Rightarrow y=\frac{x+1}{2}$. ....(1)

and $10y+x+18=10x+y$.

$9y+18=9x$

$y+2=x$

$\frac{x+1}{2}+2=x$

$x+1+4=2x$

$x-2x=-5$

$-x=-5$

$x=5$

$\Rightarrow y=\frac{5+1}{2}=\frac{6}{2}=3$.

$\therefore$ The two digit number $=10y+x$

$=10\left(3\right)+5$

$=35$.