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

Let the number be 'x ' and 'y '.Number= 10x+y According to question,10x+y/x+y=6 ----(1) => 10x+y=6x+6y => 10x-6x+y-6y=0 => 4x-5y=0 =>4x=5y----(2) Also,10x+y-9=10y+x---(3) => 10x-x+y-10y=9 => 9x-9y=9 => x-y=1 => x=1+y----(4) Putting (4) in (2) 4(1+y)=5y => 4+4y=5y => y=4 Also x=y+1 or x=4+1 or x=5 Therefore Required Number=10x+y or 10*5+4 or 50+4 or 54. Hope it helped you!!!