1. Calculate the Error Rate
The watch gains 10 seconds every 5 minutes.
First, let's find the total "watch time" that passes for every 5 minutes of "true time":
To make the units consistent:
5 min+10 sec=5+6010=5+61=631 minutes
So, 631 minutes of the Watch Time is equal to 5 minutes of the True Time.
2. Find the Total Watch Time Elapsed
The watch was set correct at 9 am.
The watch now shows 7:20 pm (20 min past 7) the same evening.
-
Time from 9 am to 12 pm = 3 hours
-
Time from 12 pm to 7:20 pm = 7 hours 20 minutes
-
Total Watch Time = 10 hours 20 minutes
Convert this total into minutes:
Total Watch Minutes=(10×60)+20=620 minutes
3. Calculate the True Time Elapsed
We use the ratio derived in step 1:
True Time=Watch Time×(Watch IntervalTrue Interval)
Substituting the values:
Now, simplify:
True Time=20×30=600 minutes
4. Determine the Actual Time
Convert the 600 minutes of True Time back into hours:
The true time is exactly 10 hours after 9 am.
Final Answer
The true time is 7 pm.
The correct option is (a).
