Question

In a two-digit number,the digit at the units place is equal to the square of the digit at tens place if 54 is added to the number the digits get interchanged find the number

Answer 1

Solution

Suppose that,

The two digit number is 10x + y

Then, the unit palace is y and tens palace is x

According to given question,

y = x2 …… (1)

Then,

Again, according to given question,

10x+y+54=10y+x

⇒10x−x+y−10y+54=0

⇒9x−9y+54=0

⇒x−y+6=0....(2)

From equation (1) to,

⇒x−x2 +6=0

⇒−x2 +x+6=0

⇒x 2 −x−6=0

⇒x 2−(3−2)x−6=0

⇒x 2 −3x+2x−6=0

⇒x(x−3)+2(x−3)=0

⇒(x−3)(x+2)=0

For,

x−3=0

x=3

Put in (2)

Then,

x−y+6=0

3−y+6=0

−y+9=0

y=9

Then,

The number is

10x+y

⇒10×3+9

⇒39

Hence, this is the answer.