Question

When riding my bike in the dark, I use two rear bike lamps. Both of the lamps are in ‘flashing mode’, which means that they repeatedly emit light for a set period of time at set intervals. One of the lamps shines for one second and goes dark for one second repeatedly; the other lamp shines for two seconds and goes dark for two seconds repeatedly. I always turn both lamps on together at the start of my ride. For how many seconds in each minute do none of the lamps shine when they are in use?
A) 10 B) 12 C) 15 D) 20 (also give reasoning)

Answer 1

Answer: c) 15

Step-by-step explanation:

You can simply make the following table :-  ( Y = Yes, N = No)

Assuming that the lamps flash the moment they're switched on..

              Light 1                   Light 2

1 sec.          Y                           N

2 sec.         N                           Y

3 sec.         Y                           Y

4 sec.         N                           N

So you notice that every four seconds, both the lamps are switched off for a period of 1 second and this order will follow throughout the minute.

We also know that there will be 15 sets of these 4 seconds in every minute.

(15 × 4 = 60)

So, in a each minute, their will be 15 seconds in which the lamps do not shine.