Question

In a two digit number the digit at the unit place is equal to the square of the digit at tens place . If 18 is addad to the number ,the digits get interchanged . Find the number.

Answer 1

let the two digits number be 10A+B,

now according to the question

B = A²,

Also

10A+B + 18 = 10B+A,

10A+B-A-10B=-18,

9A-9B=-18,

9(A-B)=-18,

then

(A-B)=-2,

put B=A² here , We get

A-A²=-2,

-A+A²=2,

then

A²-A-2=0,

(A-2)(A+1)=0,

then

A=2,

if A=2,

therefore

B=A²,

B=2²=4,

therefore

two digits number = 10A+B,

=10×2+4,

=20+4=24