Question

If the two incorrect watches are set at 12 : 00 noon at correct time, when will both the watches show the correct time for the first time given that the first watch gains 1 min in 1 hour and second watch loses 4 min in 2 hours:

• A. $6$ pm, $25$ days later
• B. $12:00$ noon, $30$ days later
• C. $12$ noon, $15$ days later
• D. $6$ am $45$ days later

Answer 1

Answer: (B)

$12:00$ noon, $30$ days later

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.

option B