Question

the difference between a two digit number and the number obtained by interchanging its digit is 27 what is the difference between the sum and the difference of the digit of the number if the ratio between the digit of number is 1 ratio 2 ​​

Answer 1

Answer:

Explanation:

Assume, the 2 digits be X and Y

So, the first 2 digit no. Is (10*X+Y)

And, the second 2 digit no. Is (10*Y+X)

Given:

Difference between first and second 2 digit no. = 27

I.e. (10*X+Y)-(10*Y+X)=27

I.e. 10X+Y-10Y-X=27

I.e. 9X-9Y=27

I.e. 9*(X-Y)=27

I.e. (X-Y)=27/9

I.e. (X-Y)=3..................NOTE it as A

Also, it's given:

Ratio between digits of first number is 2

I.e. X/Y=2

I.e. X=2Y.......NOTE it as B

Substituting the value of Y from B to equation A:

2Y - Y = 3

I.e. Y=3

From B,

X= 2Y=2*3=6

So we have X=6and Y=3

Hence first number is 10*6+3=63

Second number is 10*3+6=36

Their difference =63-36=27, which validates the first given statement in problem.

Now we know value of X and Y.

Sum of 2 digits is X+Y=6+3=9....C

Difference of 2 digits is X-Y=6-3=3...D

So ASK is:

Difference between sum and difference of these 2 digits I.e. what is C-D

I.e. 9-3=6

Hence answer is 6

Answer 2

Answer:

Explanation:

Let xy be the required two digit number.

Let the ten's digit be x.

Let the unit's digit be y.

Therefore the decimal expansion is 10x + y.

On interchanging the digits we get the expansion as 10y + x.

Given that the difference between a 2-digit number and by interchanging = 27.

(10x + y) - (10y + x) = 27

10x + y - 10y + x = 27

9x - 9y = 27

x - y = 3    -------------- (1)

Given that the ratio between the digits of a number = 2:1.

y/x = 1/2

x = 2y    ------------ (2)

substitute (2)  in (1), we get

x - y = 3

2y - y = 3

y = 3.

Substitute y = 3 in (2), we get

x = 2 * y

x = 2 * 3

x = 6.

Therefore the required number is 10x + y = 10(6) + 3

                                                                     = 63.

Verification;

63 - 36 = 27.

Hope this helps!