1
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Question

# The 2 digit number which becomes (56)th of itself when its digits are reversed. Find out the number when the difference of the digits is 1.

A
45
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B
54
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C
36
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D
None of these
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Solution

## The correct option is B 54The number becomes 56 of itself on reversing that is the reversed number is less than the original number.∴ the tens digit in the original number is greater than the unit place digit.Let the number be 10x+y, then (x−y)=1 ....given⇒x=(y+1) ....(1)Again 56(10x+y)=10y+x⇒44x=55y⇒4x=5y ....(2)Substituting for x from (1), we get4(y+1)=5y⇒y=4⇒x=y+1=5∴ the two digit number is 54.

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