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Question 54
The sum of two digits of a number is 10. If the digits are interchanged, then its value increases by 18. Find the number.
Solution
Let the digits at unit place be y and tens place be x
x + y = 10 --------I
Number formed = 10x + y and number formed after digits interchnaged = 10y + x
According to the question,
(10y+x) - (10x+y) = 18
10y + x - 10x - y = 18
9y - 9x = 18
y - x = 2 Â ----------II
Adding I and II we get
2y = 12
y = 6 and x = 4
Hence, number =Â $$10\times\ 4+6=46$$
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