A two digit number is such that 3 times the units digit exceed the tens digit by 14. If the digits are reversed, the value of the number increases by 36. Find the number
ab = 10 a +b
ba = a + 10 b = 10 a + b + 36
3 b - a = 14 so a = 3 b -14
3 b - 14 + 10 b = 30 b -140 + b + 36
18 b = 90
b = 5
a = 3*5 - 14 = 1
so
15
let the tens digit be x , 0 ≤ x ≤ 9, 0 ≤ y ≤ 9
then the unit digit is y
"3 times the units digit exceed the tens digit by 14"
---> 3y = x + 14
x = 3y - 14 , but clearly y can only be 5, 6, 7,
the original number is 10x + y
the number reversed is 10y + x
10y + x - (10x + y) = 36
9y - 9x = 36
3y - 3x = 12
sub in our previous value for x
x+14 - 3x = 12
-2x = -2
x = 1
then 1 = 3y-14
y = 5
the original number was 15