sum of the digits of a two-digit number is 9.when we interchange the digits ,it is found that the resulting new number is greater than the original number by 27.what is the two-digit number .
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Answer: 36 Was the original number.
Step-by-step explanation:
Let the original number be [(10x)+y] , 'x' is digit in tens place and 'y' is digit in units place.
ACCORDING TO FIRST CONDITION
x +y=9--->1st eqn
ACCORDING TO SECOND CONDITION
[10y+x] - [10x +y] =27 ---->2nd eqn
Simplifying 2nd equation
9y-9x=27
y-x=3---->3rd eqn
ADDING 1st and 3rd eqn
2y=12
y =6
SUBSTITUITING VALUE OF Y IN EQN 1
x=9-y
x=9-6=3
THEREFORE,Original number was 36.
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