Question

In a 2 digit number the digit at the unit place is equal to the square of the digit at tens place .if 18 is added to the number the digit get interchanged .find the numbers.

Answer 1

Answer:

Have a look at attached picture..................

Answer 2

Step-by-step explanation:

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=x

2

…… (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−x

2

+6=0

⇒−x

2

+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.