The Sum Of The Digits On A Digital Clock Is 15. The Number Of Minutes Is 5 Times The Number Of Hours What Time Is It?

Answer 1

Case1: the number of hours is single digit
hours --- h
unit digit of minutes --x
tens digit of minutes --y
x+10y = 5h **

x+y+h = 15
h = 15-x-y
5h = 75 - 5x-5y ***

equating ** and ***

x+10y = 75-5x-5y
6x + 15y = 75
2x + 5y = 25
x = (25-5y)/2
--> 25 - 5y must be even so it divides evenly by 2,
values of 25-5y , 0 ≤ y≤ 5 :
25
20 <--- y = 1 , x = 10 , not possible
15
10 <--- y = 3 , x = 5 , h = 15-3-5 = 7
5
0

the time is 7:35

check:
6+3+5 = 15 , check
35 = 5(7), check