Question

the difference between 2 digit number and number obtained by interchanging the digits is 27, if ratio between the digits of number is2:1then find difference between sum and difference of two digits of the number

Answer 1

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!

Answer 2

The difference between a 2- digit number and the number obtained by interchanging its digits is 27.


This tells us that t is larger than u, which we'll need
to know for the next part:

...the ratio between the digits of the number is 1:2 ?

Since t is larger than u we know that this means

and not




So we have the system of two equations:



Solve by substituting:





So the number is 63.