sum of 2 digits no. is 9. the sum of no. and no. formed by interchanging the digits is 99 find the number
Answers
Step-by-step explanation:
Given:-
Sum of 2 digits number is 9. the sum of number and number formed by interchanging the digits is 99 .
To find:-
Find the number ?
Solution:-
Let the two digits in the given number be X and Y
Let the digit at 10's place be X
Let the digit at 1's place be Y
The place value of X = 10×X=10X
The place value of Y = Y×1=Y
The number = 10X+Y
The number obtained by reversing the digits
= 10Y+X
Given that
Sum of the two digits = 9
X+Y = 9 ----------(1)
The sum of number and number formed by interchanging the digits = 99
10X+Y+10Y+X = 99
=> (10X+X)+(Y+10Y) = 99
=> 11X+11Y = 99
=> 11(X+Y) = 99
=> X+Y = 99/11
X+Y = 9-------(2)
From (1)&(2)
Both equations are same.
So they are consistent and dependent lines with infinitely number of solutions.
So the possible numbers are :
18,27,36,45,54,63,72,81,90
Answer:-
The possible numbers for the given problem are
18,27,36,45,54,63,72,81,90
Check:-
1)Number = 18
Sum of the digits = 1+8=9
The sum of number and number formed by interchanging the digits
18+81 = 99
2) Number = 27
Sum of the digits =2+7 = 9
The sum of number and number formed by interchanging the digits
27+72 = 99
3) Number = 36
3+6 = 9
36+63 = 99
4) Number = 45
4+5 = 9
45+54 = 99
Used Concept:-
a1x+b1y+c1=0 and a2x+b2y+c2=0 are two linear equations in two variables and a1/a2=b1/b2=c1/c2
then they are consistent and dependent lines with infinitely number of solutions.