There are two digits in a number. Their sum is 9. If 27 is added to the number, its digits get interchanged. Find the number.
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the answer is 36.......................
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let the ones place digit be y Nd tens place digit be x .
Then, no. is 10x + y
ATQ,
x+y =9
y=9-x
Also,
10x + y + 27 = 10y + x
10x-x-10y+y+27=0
9x-9y+27=0
9x-9(9-x)+27=0 (since y=9-x)
9x-81+9x+27=0
18x-54=0
18x=54
x = 3
putting X=3 in y=9-x,
y=9-3=6
So, the no. is 36
Then, no. is 10x + y
ATQ,
x+y =9
y=9-x
Also,
10x + y + 27 = 10y + x
10x-x-10y+y+27=0
9x-9y+27=0
9x-9(9-x)+27=0 (since y=9-x)
9x-81+9x+27=0
18x-54=0
18x=54
x = 3
putting X=3 in y=9-x,
y=9-3=6
So, the no. is 36
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