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31 May 2018, 12:05
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
75% (01:02) correct
25%
(00:47)
wrong
based on 113
sessions
History
Date
Time
Result
Not Attempted Yet
The circular clock above shows a time of exactly 3:30. What is the value of x?
(A) 60
(B) 75
(C) 85
(D) 90
(E) 105
Attachment:
Quant8.jpg [ 9.8 KiB | Viewed 5995 times ]
31 May 2018, 16:04
Kudos
Bookmarks
Bunuel
ans: B
at 3:30 hrs needle will be in between/mid 3 and 4 so we will find the angle from there. hour needle runs 360 in 12 hrs means 30 degree in one hour so in half hour it will run only 15 degree. now minutes needle will run for 180 degree in 30 minutes.
now we will get the angle from the 3. hrs needle will run for 15 and minutes needle will run 90 degree.
so the angle between both the needles at 3:30 will be 90-15 =75 degree.
01 Jun 2018, 03:59
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Solution
Given:
• In the given figure, the circular clock shows a time of exactly 3:30
To find:
• The value of x
Approach and Working:
Method 1: Taking the reference time as 12:00 hrs
• If we consider the movement of the minute hand and hour hand separately, with respect to 12:00 hrs, we can calculate their individual displacement
• The minute hand of a clock covers a distance of 360° in 60 minutes
- o Hence, it covers a distance of 6° in every minute
- o Hence, it covers a distance of \(\frac{1}{2}\)° in every minute
Now, after the completion of every hour, minute hand comes to 12.
• Hence, at 3:30, the movement of the minute hand = 30 * 6° = 180°
From 12:00 hrs to 3:30, the hour hand moves for a time of 3.5 hrs = 210 minutes
• Hence, at 3:30, the movement of the hour hand = 210 * \(\frac{1}{2}\)° = 105°
• Therefore, the distance in between the minute and the hour hand = x = 180° - 105° = 75°
Method 2: Taking the reference time as 3:00 hrs
At 3:00 hrs, the minute hand will be at 12 and the hour hand will point towards 3, making a gap of 90° in between
• At 3:30 hrs, the minute hand will make a movement from 12 to exact opposite at 6, hence covering a distance of \(\frac{360°}{2}\) = 180°
- o Hence, from 3, the displacement of minute hand = 180° - 90° = 90°
• Therefore, the distance between the minute and the hour hand = x = 180° - 105° = 75°
Hence, the correct answer is option B.
Answer: B
