Question

02. The sum of a two digit number and the number formed by inter-
changing its digits is 110. If 10 is subtracted from the first number,
the new number is 4 more than 5 times the sum of the digits in the
first number. The first number is :
​

Answer 1

Let the unit digit be y & tens digit be x.

Original number = (10x+y)

After interchanging the digits

New number = (10y+x)

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

11x +11y = 110

11(x+y)= 110

x+y = 110/11

x+y= 10…………...(1)

x= 10-y……………(2)

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

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

(10x+y) = 4+ 50+10

(10x+y) = 64

10(10-y) +y = 64

100-10y +y= 64

100 -9y = 64

-9y = 64-100

-9y = -36

y= 36/9= 4

y= 4

putting the value of y in eqn 2

x= 10-y

x= 10-4

x= 6

Hence , the first number is 6 & second number is 4.

Original Number is 10x+y = 10× 6+4= 60+4= 64

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Hope this will help you...

Answer 2

Let us take the number to be 10x+y; then,

10x+y+10y+x = 110

or, 11x+11y = 110

or, x = (110-11y)/11

or, x = 11(10-y)/11 = 10-y ....(1)

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

or, 10(10-y)+y-10 = 5(10-y+y)+4

or, 100 - 10y + y -10 = 54

or, -9y = - 36

or, y = 4

Hence, x = 6 and y = 4

And the number is 64.

HOPE THIS COULD HELP!!!