Question

1 ) A two digit number and the number with digits interchanged add up to 154. In the given number the digit in unit's place is 2 more than the digit in the tens place . Find the original number .​

Answer 1

Solution :-

Let us assume that,

=> 'x' be the number in unit's place.

=> 'y' be the number in ten's place.

Thus, Number will be '10y + x'

After, interchanged the number will be '10x + y'.

Now, given that, A two digit number and the number with digits interchanged add up to 154.

=> 10x + y + 10y + x = 154

=> 11x + 11y = 154

=> x + y = 154/11 = 14 …(1)

Also given that, In the given number the digit in unit's place is 2 more than the digit in the ten's place.

So, digit in unit's place = digit in ten's place+2

=> x = y+2

=> x - y = 2 …(2)

Now, Adding (1) and (2) we get :

x + y = 14

+ x - y = 2

____________

2x = 16

Therefore, x = 16/2 = 8

Then, Putting the value of 'x' in equation(1) we get :-

=> 8 + y = 14

=> y = 14-8 = 6

The original number is 10y + x

=> 10(6) + 8

=> 60 + 8

=> 68

Hence, The Original Number is 68.