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 numbers.

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
.

substitute the above into:
4y = 5x+4
4y = 5(y-2)+4
4y = 5y-10+4
4y = 5y-6
4y+6 = 5y
6 = y
.
substitute above into:
4y = 5x+4
4(6) = 5x+4
24 = 5x+4
20 = 5x
4 = x
.
The number is 64

Answer 2

Step-by-step explanation:

let the the digit = x

and the unit digit = y

number = 10x+y

when digit are reversed then no. = 10y+x

1 condition

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

x+10y = 6x+6y+4

10y-6y = 6x -x+ 4

4y = 5x +4 ...........................(1)

2 condition

x+10y-18 =y+10x-x

9y-18 = 9x

y-2 = x........................................(2)

substituting the value of x in equation 1

4y = 5x + 4

4y = 5(y-2)+4

4y = 5y -10 +4

4y = 5y-6

4y-5y =-6

-y = -6

y= 6

Putting the value of y in equation 2

y - 2 = x

6 - 2 = x

4 = x

The no. is 46

and reversed no. is 64

I hope it helps you