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Question
The sum of a two-digit number and the number obtained by reversing the digits is 110 and the difference of two digits is 2. Find the number.
Solution
Let x be the digit at ten's place and y be the digit at unit's place.
Then, the number is 10x + y.
Number obtained by reversing the digit = 10y + x
According to given information, we have
(10x + y) + (10y + x) = 110
⇒ 11x + 11y = 110
⇒ 11(x + y) = 9
⇒ x + y = 10 ....(i)
Also, x - y = 2 ....(ii)
Adding eqns. (i) and (ii), we get
2x = 12
⇒ x = 6
⇒ 6 + y = 10
⇒ y = 4
∴ Required number
= 10x + y
= 10 x 6 + 4
= 60 + 4
= 64.
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