Question

a number consists of two digits where the number is divided by the sum of its digits the quotient is 7. if 27 is subtracted from the number the digits interchange their places find the number

Answer 1

Answer:

The number is 63

Step-by-step explanation:

according to first condition, if digits are x and y ;x>y then

let 10x+y be the required number

10x+y/x+y=7

=>10x+y=7x+7y

=>3x=6y

=>x=2y                                          .....(1)

the next condition says that when 27 is subtracted from 10x+y i.e.

10x+y-27 it will give a number who has the same digits but interchanged

so =>10x+y-27=10y+x

=>9x-9y-27=0 ....(2)

=>x-y-3=0        [(2) divided by 9]

=>x-y=3    putting value from (1)

=>2y-y=3=y

therefore y=3

putting this in (1) we get x=6

10(6)+3 is the number

63 is the required number

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