Question

Sum of digits of two digit number is 8 when we interchange the digit it is found that the resulting new number is greater than the original bnumber by 18.what is the two digit number.

Answer 1

Let the no. at unit place of the two digits no. be x.

So, as the sum of digits is 8

so, the digit at the tens place will be (8-x)

so, the no. comes out to be 10(8-x) + x.

or, the no. is 80-10x +x = 80 - 9x

Now , we interchange the digits.

so, the digit at unit place is (8-x)

and at tens is x

hence the new no. is 10x + (8-x) = 9x + 8

According to the question;

( 9x + 8 ) = ( 80 - 9x ) + 18

or, 9x + 8 = 98 - 9x

or, 18x = 90

so, x = 90/18 = 5

Hence. no. is 80 -9(5)

= 80 - 45

= 35.

Answer 2

Answer:

the two digit required number is 35

Step-by-step explanation:

as per the question asked,

we need to find a number such that Sum of digits of two digit number is 8 when we interchange the digit it is found that the resulting new number is greater than the original number by 18

so we assume that the no. at unit place of the two digits no. be x.

So, as the sum of digits is 8

which clearly makes that the digit at the tens place will be (8-x)

the general form of a number ab is 10a+b

so as per this,

the no. comes out to be 10(8-x) + x.

the no. is 80-10x +x = 80 - 9x

Now , when we interchange the digits.

so, the digit at unit place is (8-x)

and at tens is x

hence the new no. is 10x + (8-x) = 9x + 8

According to the question;

the difference between the original and exchanged digit number is

( 9x + 8 ) = ( 80 - 9x ) + 18

or, 9x + 8 = 98 - 9x

or, 18x = 90

so, x = 90/18 = 5

Hence the required no. is 80 -9(5)

= 80 - 45

= 35.

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