A number consists of two digits.When it is divided by the sum of its digits,the quotient is 6 with no remainder.When the number is diminished by 9, the digits are reversed.Find the number.

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Solution

Let x be the digits at tens place and y be the digit at one's place.

According to question,
$fraction numerator 10 x plus y over denominator x plus y end fraction equals 6 10 x plus y equals 6 x plus 6 y 4 x minus 5 y equals 0$
4x-5y=0..........(1)

Condition 2
10x+y-9=10y+x
9x-9y=9
x-y=1.........(2)
Solving eq 1 and eq 2
y=4
Putting value in eq 2
x=5
So the number is 54.

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A number consists of two digits.When it is divided by the sum of its digits,the quotient is 6 with no remainder.When the number is diminished by 9, the digits are reversed.Find the number.

Let x be the digits at tens place and y be the digit at one's place. According to question, 4x-5y=0..........(1) Condition 2 10x+y-9=10y+x 9x-9y=9 x-y=1.........(2) Solving eq 1 and eq 2 y=4 Putting value in eq 2 x=5 So the number is 54.