XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 8 : Kim's wristwatch always shows the correct time, including 'am' and 'pm'. Jim's watch is identical to Kim's watch in all aspects except its pace, which is slower than the pace of Kim's watch. At 12 noon on January 1st, Jim sets his watch to the correct time, but an hour later, it shows 12:57 pm. At 12 noon on the next June 1st, Jim resets his watch to the correct time.

On how many instances between, and including 12 noon on the two dates mentioned, do Jim's and Kim's watches show the exact same time, including the 'am' and the 'pm'?

Video Explanation

Explanatory Answer

At 12 noon on January 1st, Jim sets his watch to the correct time, but an hour later, it shows 12:57 pm.
So, Jim’s watch loses 3 mins for 1 hour.
To show the correct time again Jim’s watch should lose 24hrs.
To loose 24hrs, it needs 480hrs (means 20days)
For every 20 days, both watches show the same time.
From Jan01st to june01st(noon) we have 151 days.
The both watches should show correct time in \(\frac{151}{20}\) times.
Jim's and Kim's watches show the exact same time including 12 noon on the two dates mentioned is 7 + 2 = 9 times

The answer is '9'

Choice A is the correct answer.