sum of the digits of a two digit number is 11. when we interchange the digits, it is found that the resulting number is greater than the original number by 63. find the two digit number.
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sum of the digits of a two digit number is 11. when we interchange the digits, it is found that the resulting number is greater than the original number by 63. find the two digit number.
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sum of the digits of a two digit number is 11. when we interchange the digits, it is found that the resulting number is greater than the original number by 63. find the two digit number.
ANSWER
let the numbers are x,y respectively
x+y=11. EQ ...(1)
(10x+y)-(10y+x) = 63or
9x-9y = 63or
Add (1) and (2)
so
x=9
and y=11-x
y=11-9
y=2
so number is
10x+y
=10(9)+2
=90+2
=92
VERIFICATION
sum of numbers are
9+2=11
10x+y=92
and
10y+x=22+9=29
=>
(10x+y)-(10y+x) = 92-29
(10x+y)-(10y+x) = 63
hence proved