SOLUTION: The sum of a number of two digits & the number obtained on inter� changing the digits is 99. If 5 is added to the number , then it is 4 less than 6 times the sum of the digits. F

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Question 876529: The sum of a number of two digits & the number obtained on inter�
changing the digits is 99. If 5 is added to the number , then it is 4 less
than 6 times the sum of the digits. Find the number
Answer by mananth(16946) (Show Source):
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Let the number be xy
10x+y+10y+x=99
11x+11y=99
/11
x+y=9.....................(1)
ii condition
10x+y+5 = 6(x+y)-4
10x+y+5=6x+6y-4
4x-5y=-9..................(2)
solve (1) &(2)
1 x + 1 y = 9 .............1

4 x -5 y = -9 .............2
-5 y
multiply (1)by 5
Multiply (2) by 1
5 x 5 y = 45
4 x -5 y = -9
Add the two equations
9 x = 36
/ 9
x = 4
plug value of x in (1)
1 x + 1 y = 9
4 + y = 9
y = 9 -4
y = 5
y = 5
the number is 45