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.
Answers
Let the two digit number be : AB
Mentioned : Sum of digits of the two digit number is 15
A + B = 15
A = 15 - B
After interchanging, The New number will be : BA
♣ New Interchanged number exceeds Original number by 9
BA - AB = 9
● BA can be written as 10B + A
● AB can be written as 10A + B
10B + A - [10A + B] = 9
10B - 10A + A - B = 9
9B - 9A = 9
B - A = 1
Substitute value of A = 15 - B in above Equation
B - [15 - B] = 1
B - 15 + B = 1
2B = 15 + 1
2B = 16
B = 8
Substitute B = 8 in Equation A = 15 - B
A = 15 - 8
A = 7
Original Number = 78
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