Question

A two-
-digit numbert is 4 times the sum of its digits)
if 18 is added to the number the digits
digits
are refer-
sed, find the number.​

Answer 1

Answer:

Let unit's digit =y and the ten's digit =x

So, the original number =10x+y

The sum of the two digit number =10x+y

The sum of the digit =x+y

According to the question, (10x+y)=4(x+y)

⇒10x+y=4x+4y

⇒10x−4x+y−4y=0

⇒6x−3y=0

⇒2x−y=0

⇒y=2x….(i)

After interchanging the digits,

New number =x+10y and 10x+y+18=x+10y

⇒10x+y+18=x+10y

⇒10x−x+y−10y=−18

⇒9x−9y=−18

⇒x−y=−2…(ii)

On substituting the value of y=2x in Eq. (ii),we get

x−y=−2

⇒x−2x=−2

⇒−x=−2

⇒x=2

On putting the value of x=2 in Eq. (i), we get

y=2×2=4

So, the Original number =10x+y

=10×2+4

=20+4

=24

Hence, the two digit number is 24.