Question

The sum of a two digit number and the number formed by interchanging the digit is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of its digits in the first number. Find the first number

Answer 1

Given:

Sum of two -digit number and number formed by interchanging the digit=110.

If 10 is subtracted from the first number, the new number= 4+5(x+y)

To Find:

The first number.

Solution:

Let the two-digit number be (10x+y)

The number formed by interchanging the digits=(10y+x)

According to question,

(10x+y)+(10y+x)=110.

=11x+11y=110.

=11(x+y)=110.  

=x+y=10      ....equation(1).

Also,

(10x+y)-10=4+5(x+y)

=10x+y-10=4+5(10)     (from equation(1)

=10x+y=4+50+10

=10x+y=64.

Therefore, the required number is 64.