IPMPrepA watch loses 6 minutes every 24 hours. It is set right at noon on Monday. How many minutes behind will it be after 48 hours?
Solution
It loses 6 minutes in 24 hours, so in 48 hours it loses 6 × 4824 = 12 minutes.
Answer: (D) 12 minutes
Logical Reasoning and Data Interpretation · Clocks and calendars
Clocks: IPMAT practice questions
24 questions. Each is marked with the exam level it suits. Answer, then open the step-by-step solution.
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At what time between 9 and 10 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 9:00 the hour hand is 270° ahead.
Time = 270 ÷ 5.5 = 49 111 minutes past 9.
Answer: (B) 49 111 minutes past 9
How many times are the hands of a clock at right angles in 12 hours?
Solution
In 12 hours the hands coincide 11 times and are opposite 11 times (not 12, because one meeting is shared between two hours), and they are at right angles 22 times.
A day has two 12-hour cycles.
So the answer is 22.
Answer: (D) 22
At what time between 4 and 5 o'clock will the hands of a clock first be at right angles?
Solution
Right angle means a 90° gap. At 4:00 the gap is 120°; the minute hand gains 5.5° per minute.
The first time the gap is 90° is after (120 − 90) ÷ 5.5 = 5 511 minutes.
Answer: (C) 5 511 minutes past 4
A clock loses 6 minutes every hour. It is set right at 9:00 a.m. What is the correct time when the clock shows 3:00 p.m.?
Solution
For every 60 minutes of real time the clock moves 54 minutes.
The clock has moved 360 minutes, so the real time passed is 360 × 6054 = 400 minutes.
Correct time = 9:00 a.m. + 400 minutes = 3:40 p.m.
Answer: (C) 3:40 p.m.
A clock shows 6:10. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60.
11:60 − 6:10 = 5:50.
Answer: (C) 5:50
What is the reflex angle between the hands of a clock at 9:25?
Solution
The smaller angle is |30 × 9 − 5.5 × 25| = 132.5°.
Reflex angle = 360° − 132.5° = 227.5°.
Answer: (D) 227.5°
A clock takes 21 seconds to strike 4 o'clock. How long will it take to strike 12 o'clock?
Solution
Striking 4 has 3 gaps, so each gap is 213 = 7 seconds.
Striking 12 has 11 gaps: 11 × 7 = 77 seconds.
Answer: (D) 77 seconds
What is the angle between the hour and minute hands of a clock at 9:30?
Solution
Angle = |30H − 5.5M| = |30 × 9 − 5.5 × 30| = 105°.
Answer: (D) 105°
Through how many degrees does the hour hand of a clock turn in 5 hours 42 minutes?
Solution
The hour hand turns 30° per hour, that is 0.5° per minute.
342 minutes × 0.5° = 171°.
Answer: (C) 171°
What is the reflex angle between the hands of a clock at 11:40?
Solution
The smaller angle is |30 × 11 − 5.5 × 40| = 110°.
Reflex angle = 360° − 110° = 250°.
Answer: (A) 250°
What is the angle between the hour and minute hands of a clock at 7:10?
Solution
Angle = |30H − 5.5M| = |30 × 7 − 5.5 × 10| = 155°.
Answer: (A) 155°
At what time between 3 and 4 o'clock will the hands of a clock point in opposite directions?
Solution
The hands are opposite when the minute hand is 180° ahead of the hour hand.
Gap to make up = 90 + 180 = 270°, at 5.5° per minute.
Time = 270 ÷ 5.5 = 49 111 minutes past 3.
Answer: (D) 49 111 minutes past 3
A clock shows 2:45. What time does its mirror image show?
Solution
For a mirror image, subtract the time from 11:60.
11:60 − 2:45 = 9:15.
Answer: (B) 9:15
At what time between 4 and 5 o'clock will the hands of a clock point in opposite directions?
Solution
The hands are opposite when the minute hand is 180° ahead of the hour hand.
Gap to make up = 120 + 180 = 300°, at 5.5° per minute.
Time = 300 ÷ 5.5 = 54 611 minutes past 4.
Answer: (C) 54 611 minutes past 4
A clock loses 6 minutes every hour. It is set right at 7:00 a.m. What is the correct time when the clock shows 1:00 p.m.?
Solution
For every 60 minutes of real time the clock moves 54 minutes.
The clock has moved 360 minutes, so the real time passed is 360 × 6054 = 400 minutes.
Correct time = 7:00 a.m. + 400 minutes = 1:40 p.m.
Answer: (D) 1:40 p.m.
A clock takes 20 seconds to strike 5 o'clock. How long will it take to strike 12 o'clock?
Solution
Striking 5 has 4 gaps, so each gap is 204 = 5 seconds.
Striking 12 has 11 gaps: 11 × 5 = 55 seconds.
Answer: (A) 55 seconds
A watch loses 6 minutes every 24 hours. It is set right at noon on Monday. How many minutes behind will it be after 108 hours?
Solution
It loses 6 minutes in 24 hours, so in 108 hours it loses 6 × 10824 = 27 minutes.
Answer: (C) 27 minutes
Through how many degrees does the hour hand of a clock turn in 3 hours 18 minutes?
Solution
The hour hand turns 30° per hour, that is 0.5° per minute.
198 minutes × 0.5° = 99°.
Answer: (D) 99°
What is the reflex angle between the hands of a clock at 1:50?
Solution
The smaller angle is |30 × 1 − 5.5 × 50| taken the short way = 115°.
Reflex angle = 360° − 115° = 245°.
Answer: (A) 245°
How many times do the hands of a clock coincide in a day?
Solution
In 12 hours the hands coincide 11 times and are opposite 11 times (not 12, because one meeting is shared between two hours), and they are at right angles 22 times.
A day has two 12-hour cycles.
So the answer is 22.
Answer: (A) 22
At what time between 2 and 3 o'clock will the hands of a clock first be at right angles?
Solution
Right angle means a 90° gap. At 2:00 the gap is 60°; the minute hand gains 5.5° per minute.
The first time the gap is 90° is after (60 + 90) ÷ 5.5 = 27 311 minutes.
Answer: (A) 27 311 minutes past 2
What is the angle between the hour and minute hands of a clock at 5:24?
Solution
Angle = |30H − 5.5M| = |30 × 5 − 5.5 × 24| = 18°.
Answer: (D) 18°
At what time between 8 and 9 o'clock will the hands of a clock coincide?
Solution
The minute hand gains 5.5° per minute on the hour hand. At 8:00 the hour hand is 240° ahead.
Time = 240 ÷ 5.5 = 43 711 minutes past 8.
Answer: (D) 43 711 minutes past 8
These are original practice questions written by Target Campus in the pattern, syllabus and difficulty of IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT and SET. They are not previous-year papers.