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Question

# A two digits number becomes 56th of itself when its digits are reversed. If the difference of the digits is 1, then the number is

A
45
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B
54
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C
56
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D
65
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Solution

## The correct option is B 54Let the units digit be 'y' Let the tens digit be 'x' Two digit no = 10x+y Reversed no = 10y + x According to the question, Reversed no = 56(Two digit no) ⇒10y+x=56(10x+y) ⇒6(10y+x)=5(10x+y) ⇒60y+6x=50x+5y ⇒60y−5y=50x−6x⇒55y=44x 5y=4x⇒5y−4x=0......(1) Case 1 x−y=1 ⇒x=1+y .........(2) Substituting x = 1+y from (2) in (1) 5y−4x=0 ⇒5y−4(1+y)=0 ⇒5y−4−4y=0 ⇒y=4 ∴x=1+y (from (2)) x=1+4=5 Case 2 y−x=1 ⇒y=1+x........(3) Substituting y=1+x from (3) in (1) 5y−4x=0 ⇒5(1+x)−4x=0 ⇒5+5x−4x=0 ⇒5+x=0 ∴x=−5 Required two digit number =10x+y =10(5)+4 =54

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