What time between 3 and 4 oclock will the minute hand and the hour hand are on the same straight line but facing opposite directions?

Option 4 : \(5\frac{5}{{11}}\) Minutes past 7

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The two hands of a clock will be in the same straight line but not together between H and (H + 1) o' clock at

\(\left\{ {\begin{array}{*{20}{c}} {\left( {5H - 30} \right)\;\frac{{12}}{{11}}}\\ {Minutes\;past\;H,\;when\;H > 6\;}\\ \;\\ {\left( {5H + 30} \right)\frac{{12}}{{11}}}\\ {minutes\;past\;H.\;when\;H < 6}\\ \; \end{array}} \right.\)

Here H = 7

Hands of the clock will point in opposite directions at

= (5 × 7 - 30)12/11 minutes past 7

= 5 × 12/11 minutes past 7

= 60/11 minutes past 7

\(5\frac{5}{{11}}\) minutes past 7.

Hence, the correct answer is 5(5/11) minutes past 7.

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Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

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12.	The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
A. 80° B. 75° C. 60° D. 105° Answer: Option B Explanation: Angle traced by hour hand in 17 hrs = 360 x 17 ° = 255°. 2 12 2 Angle traced by min. hand in 30 min. = 360 x 30 ° = 180°. 60 Required angle = (255 - 180)° = 75°.

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Page 2

Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

16.	At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
A. B. C. D. Answer: Option D Explanation: At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand. To be coincident, it must gain 15 min. spaces. 55 min. are gained in 60 min. 15 min. are gained in 60 x 15 min = 16 4 min. 55 11 The hands are coincident at 16 4 min. past 3. 11

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17.	How many times do the hands of a clock coincide in a day?
Answer: Option C Explanation: The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). AM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 PM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 The hands overlap about every 65 minutes, not every 60 minutes. The hands coincide 22 times in a day.

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Page 3

Exercise :: Clock - General Questions

• Clock - Important Formulas
• Clock - General Questions

6.	At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
A. 5 min. past 7 B. C. D. Answer: Option D Explanation: When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart. At 7 o'clock, they are 25 min. spaces apart. Minute hand will have to gain only 5 min. spaces. 55 min. spaces are gained in 60 min. 5 min. spaces are gained in 60 x 5 min = 5 5 min. 55 11 Required time = 5 5 min. past 7. 11

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7.	At what time between 5.30 and 6 will the hands of a clock be at right angles?
A. B. C. 40 min. past 5 D. 45 min. past 5 Answer: Option B Explanation: At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min. 40 min. spaces are gained in 60 x 40 min = 43 7 min. 55 11 Required time = 43 7 min. past 5. 11

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