# 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 digits are reversed. Find the number.

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by dweejareddy

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by dweejareddy

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The Brainliest Answer!

'.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!!!

See the attachment below for the solution