Question

a number lying between 10 to 100 is seven times the sum of its digits. . if 9 is subtracted from it , the digits of the number are reserved then the number ​

Answer 1

Answer:

21

Step-by-step explanation:

The number is 21.

.A number of two digits

.A number of two digits10x+y

.A number of two digits10x+yis seven times the sum of its digit.

times the sum of its digit.10x+y=7(x+y)

(x+y)10x+y=7x+7y

yIf 9 is subtracted from the number, the digits are reversed.

yIf 9 is subtracted from the number, the digits are reversed.10x+y-9=10y+x

yIf 9 is subtracted from the number, the digits are reversed.10x+y-9=10y+xWhat is the number?

yIf 9 is subtracted from the number, the digits are reversed.10x+y-9=10y+xWhat is the number?10x-x+y-9=10y+x-x

yIf 9 is subtracted from the number, the digits are reversed.10x+y-9=10y+xWhat is the number?10x-x+y-9=10y+x-x9x+y-y-9=10y-y

yIf 9 is subtracted from the number, the digits are reversed.10x+y-9=10y+xWhat is the number?10x-x+y-9=10y+x-x9x+y-y-9=10y-y(9x-9)/9=9y/9

yIf 9 is subtracted from the number, the digits are reversed.10x+y-9=10y+xWhat is the number?10x-x+y-9=10y+x-x9x+y-y-9=10y-y(9x-9)/9=9y/9y=x-1

yIf 9 is subtracted from the number, the digits are reversed.10x+y-9=10y+xWhat is the number?10x-x+y-9=10y+x-x9x+y-y-9=10y-y(9x-9)/9=9y/9y=x-110x+y=7x+7y

y10x+x-1=7x+7(x-1)

11x-1 = 7x+7x-7

11x-1 = 14x-7

-1+7 = 14x-11x

6 = 3x

6 =x

3

x = 2

10x+y=7x+7y

10×2+y = 7×2 +7y

20+y = 14+7y

20-14 = 7y-y

6 = 6y

6 = y

6

y = 1

Verify

10x+y = 7x+7y

7x = 14

7y = 7

20+1 = 14+7

21

10x+y-9 = 10y+x

20+1-9 = 10+2

12

So the number is 21.

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Answer 2

suppose number is 10x+y

so 10x+y=7(x+y)

so 3x=6y

so x=2y

10x+y-9=10y+x

20y+y-9=10y+2y

so 9y=9

so y=1 and x=2 so number is 21