In a number of two digits the ratio of digit in tenth place and the digit in unit place is 2:1 If 6 is added to the three times of the sum of the digits then the opposite number is formed Find the sum of the digits of the number
x = digit in tenth place
y = digit in unit place
Number is:
10 x + y
The ratio of digit in tenth place and the digit in unit place is 2:1, means:
x = 2 y
If 6 is added to the three times of the sum of the digits then the opposite number is formed, means:
3 ( x + y ) + 6 = 10 y + x
Replace x by 2y in tis equation.
3 ( 2 y + y ) + 6 = 10 y + 2 y
3 • 3 y + 6 = 12 y
9 y + 6 = 12 y
Subtract 9 y to both sides.
6 = 3 y
3 y = 6
y = 6 / 3
y = 2
x = 2 y = 2 • 2
x = 4
Number is 42.
Sum of the digits = x + y = 4 + 2 = 6
unit digit ---- x
tens digit ---- y
x:y = 2:1
x =2y
3(x+y) + 6 = -10y - x
4x + 13y = -6
8y + 13y = -6
y is not a whole number, so the question is bogus
the original number is 42
check
sum 0f digits = 6
3times plus 6 = 18+6 = 24
which is the original number reversed (not opposite, that would be -42)
did you mean " ... then the number reversed is formed
if so ....3(x+y) + 6 = 10y + x
2x - 7y = -6
4y - 7y = -6
y = 2
then x = 4