If two incorrect watches are set at 12:00 noon at correct time, when will both watches show the correct time for the first time given that the first watch gains 1 min in one hour and second watch looses 4 min in two hours.

A. 6 PM, 25 days later

B. 12 noon, 30 days later

C. 12 noon, 15 days later

D. 6 AM, 45 days later

E. None of these

Answer: Option B

Solution(By Examveda Team)

First watch:
It shows correct time when it creates difference of 12 hours.
So, to create difference of 12 hour, time required = $$\frac{{60 \times 12}}{{24}}$$   = 30 days

Second watch:
It shows correct time when it creates difference of 12 hours.
So, to create difference of 12 hour, time required = $$\frac{{30 \times 12}}{{24}}$$   = 15 days
Now, LCM of 30 and 15 gives the time when they show correct time together. Thus, required time = 30 days, at same time.