Question
A two digit number is such that the product of its digits is 12. When 9 is added to the number, the digits interchange their places. The number is ___.
Answer:
:
Let the two digit number be ab.
a×b=12
When 9 is added to the number
10a+b+9=10b+a
9a−9b+9=0
a−b+1=0
a−12a+1=0
a2+a−12=0
(a+4)(a−3)=0
a = -4 is not accepted. So, a = 3, b = 4
The number is 34 .
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:
Let the two digit number be ab.
a×b=12
When 9 is added to the number
10a+b+9=10b+a
9a−9b+9=0
a−b+1=0
a−12a+1=0
a2+a−12=0
(a+4)(a−3)=0
a = -4 is not accepted. So, a = 3, b = 4
The number is 34 .
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