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Question

A two digit number becomes five sixth of itself when its digits are reversed the two digit differ by 1 find the number

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Solution

Let the digit in the tens place be x and ones place be y

Hence the number =(10×x)+y=10x+y

Number obtained by reversing the digits =10y+x

Given that 10y+x=(5/6)×(10x+y)

⇒60y+6x=50x+5y

⇒44x–55y=0

⇒4x–5y=0 ... (1)

It is also given that difference of digits is 1.

⇒x–y=1... (2)

Multiplying equation (2) with 4, we get

⇒4x–4y=4... (3)

On subtracting (1) and (3)

⇒4x–5y−4x+4y=0−4

⇒–y=–4

∴y=4

Putting y=4 in (1) we get

⇒4x–5y=0

⇒4x=5(4)

∴x=5

The number is 54.


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