Question

The sum of the digitof a two digit no. is 15 .The no. obtsined by interchanging the digits exceeds the given no by 9 .Find the no.​

Answer 1

Let the two digit number be : AB

Mentioned : Sum of digits of the two digit number is 15

$\longrightarrow$  A + B = 15

$\longrightarrow$  A = 15 - B

After interchanging, The New number will be : BA

♣  New Interchanged number exceeds Original number by 9

$\longrightarrow$  BA - AB = 9

●  BA can be written as 10B + A

●  AB can be written as 10A + B

$\longrightarrow$  10B + A - [10A + B] = 9

$\longrightarrow$  10B - 10A + A - B = 9

$\longrightarrow$  9B - 9A = 9

$\longrightarrow$  B - A = 1

Substitute value of A = 15 - B in above Equation

$\longrightarrow$  B - [15 - B] = 1

$\longrightarrow$   B - 15 + B = 1

$\longrightarrow$  2B = 15 + 1

$\longrightarrow$  2B = 16

$\longrightarrow$  B = 8

Substitute B = 8 in Equation A = 15 - B

$\longrightarrow$  A = 15 - 8

$\longrightarrow$  A = 7

$\longrightarrow$  Original Number = 78

Answer 2

Answer:78

Step-by-step explanation:

Given : Sum of two digit of a number = 15

let these two digits be X and Y.

A/Q

X+Y =15

X = 15 - Y ------(1)

Now, when the digits are reversed, the new number becomes YX.

A/Q

New number - old number =9

YX - XY =9

Now YX can be written as 10Y + X and XY can be written as 10X + Y.

[10Y + X ] - [10X + Y] =9

10 Y + X -10 X - Y =9

9Y - 9X = 9

9 (y-x) = 9

y- x = 1

y -1 = x ----(2)

Now, from equation 1 and 2

15 - y = y-1

15 + 1 = y+y

16 =2y

16/2 = y

8 = y

x=15 - y (from equation 1)

X =15-8

X=7

, So the original number = XY

=78