Question

a two digit number is 4 more than 6 times the sum of its digits. if 18 is subtracted from the number, the digits are reversed.find the number

Answer 1

Let x = ones digit
and y = tens digit
then from "a two digit number is 4 more than six times the sum of its digits":
x + 10y = 6(x+y)+4
x + 10y = 6x+6y+4
10y = 5x+6y+4
4y = 5x+4
.
and, from "if 18 is subtracted from the number,the digits are reversed.find the number"
x+10y -18 = y+10x
10y -18 = y+9x
9y -18 = 9x
y -2 = x
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Answer 2

let the two digit no. be xy
A.T.Q
xy = 6(x+y)+4
xy can be written as 10x+y
so it becomes
10x+y = 6x+6y+4
10x-6x = 6y-y+4
4x = 5y+4 ------------(1)
then another eq. is
xy-18 = yx
10x+y-18 = 10y+x
10x-x = 10y-y+18
9x = 9y+18
taking 9as common from R.H.S
9x=9(y+2)
dividing both sides by 9 ,we get
x = y+2 -----------(2)
putting the value of x in eq. (1) , we get
4(y+2) = 5y +4
4y+8 = 5y+4
5y-4y=8-4
y = 4
then putting this value in eq.(2) ,we get
x =y+2
x = 4+2
x=6