Question

a two digit number is four mour than 6 times the sum of its digit.if 18 is subtracted from the number.the digits are reversed.find the number



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Answer 1

Given :

a two digit number is four mour than 6 times the sum of its digit

if 18 is subtracted from the number.the digits are reversed

Answer :

Let the number = 10x + y

10x + y = 6( x+y ) +4

10x + y = 6x + 6y +4..............equation 1

(10x + y) - 18 = 10y + x.......... equation 2

(10x + y) - (10y+x) = 18

9x - 9y = 18

9 (x - y) =18

x - y = 18/9

x - y = 2........ equation 3

According to equation 1,

we can use 6x +6y +4 instead of 10x + y

(10x + y) - 18 = 10y + x

(6x + 6y +4) - 18 = 10y +x

(6x + 6y +4) - (10y+x) = 18

5x - 4y + 4= 18

5x - 4y = 14

(5x - 4y) - 4(x-y) = 14 - (4×2)

5x - 4y - 4x + 4y = 14 - 8

x = 6

According to equation 3,

6 - y = 2

6 - 2 = y

y = 4

The number = 10x + y

The number = 10× 6 + 4

= 64

Hope this will help.....