Question

2. The sum of a two digit number and the number formed by interchanging it's digits is 88. If the sum
of the sum and difference of the digits of the number is 8, what is the number?
(a) 44
(b) 17
(c) 53
(d) 80​

Answer 1

Answer:

Let the tens digit of the required number be x and the units digit be y. Then,

x+y=12 .........(1)

Required Number = (10x+y).

Number obtained on reversing the digits = (10y+x).

Therefore,

(10y+x)−(10x+y)=18

9y−9x=18

y−x=2 ..........(2)

On adding (1) and (2), we get,

2y=14⟹y=7

Therefore,

x=5

Hence, the required number is 57.

Answer 2

Step-by-step explanation:

Let the no. is of the form 10x+y

After interchenging,

The no. became,

10y+x

A/Q,

10 x+y+10y+x= 88

=> 11x + 11y = 88.....(1)

and,

(x+y) + (x-y) = 8

=> 2x = 8 => x = 4

then, 11x + 11y = 88

=> 11y = 88 - 44

=> y = 44/11 = 4

So the two digit no. is 44

ANS. option (a) 44