Question

A no. Consists of 2 digits whose sum of digits is 8. If 18 is added to the no. The digits interchange their places. Find no.

Answer 1

$\huge \boxed{\pink\star\mathfrak\orange{\large{\underline{\underline{Answer!}}}} }$

Let the unit's digit be x

Then, ten's digit= 8-x

Number= (8-x)×10+x

= 80-10x+x

= 80-9x

On interchanging the digits, unit's digit= 8-x

and ten's digit= x

New number= x×10+(8-x)

= 10x+8-x

= 9x+8

Now, According to the question

80-9x+18= 9x+8

⟹80+18-8=9x+9x

⟹18x= 90

⟹$\bold{x=\frac{90}{18}}$

⟹$\boxed{\bold\red{x= 5}}$

Unit's digit= 5

Ten's digit= 8-5=3

$\huge\boxed{\bold\red{Number= 35}}$

$\huge \boxed{\red\star\mathfrak\purple{\large{\underline{\underline{Verification!}}}} }$

35+18= 53, digits have interchanged their places.