Clock and Calendar Aptitude MCQ Questions with Answers Set 02

Answer: (b) 2 hours 30 minutes

Explanation:
1. For a mirror image, actual time = 12:00 − mirror time (when the mirror time is between 1:00 and 11:00).
2. Actual time = 12:00 − 9:30 = 2:30.
3. So the clock actually shows 2 hours 30 minutes.

Teacher's Note:
1. Mirror time and actual time always add up to 12:00 (use 24:00 if the sum of the given times is past 12).
2. You can check by drawing the hands and flipping them left to right.

Answer: (d) Loses 73²⁵¹/₂₅₃ minutes

Explanation:
1. In a correct clock the hands coincide every 65⁵/₁₁ = 720/11 minutes.
2. Here they coincide every 69 minutes, which is longer, so the clock loses: 69 − 720/11 = 39/11 minutes in every 69 minutes.
3. Loss per day = (39/11) × (1440/69) = 18720/253 = 73²⁵¹/₂₅₃ minutes.

Teacher's Note:
1. Correct hands coincide every 65 5/11 minutes; a shorter gap means the clock gains, a longer gap means it loses.
2. Gain or loss per day = (65 5/11 − gap) ÷ gap × 1440 minutes.

Answer: (d) 197¹/₂°

Explanation:
1. Hour hand: 30 × 10 + 0.5 × 25 = 312.5° from 12.
2. Minute hand: 6 × 25 = 150° from 12.
3. Angle between them = 312.5 − 150 = 162.5°, so the reflex angle = 360 − 162.5 = 197.5°.

Teacher's Note:
1. A reflex angle is the larger angle (more than 180°), so subtract the smaller angle from 360°.
2. Measure both hands from the 12 mark, then subtract.

Answer: (b) 67¹/₂°

Explanation:
1. Angle = |30H − 5.5M| with H = 5, M = 15.
2. = |150 − 82.5| = 67.5°.

Teacher's Note:
1. Use the formula angle = |30H − 5.5M|; if the result exceeds 180°, subtract it from 360°.
2. Remember the hour hand moves 0.5° per minute, so it is never exactly on the hour mark except at full hours.

Answer: (b) 44

Explanation:
1. The hands are at right angles twice every hour, except that the 3 o'clock and 9 o'clock positions are each shared by two hours.
2. So in 12 hours there are 22 right angles, and in 24 hours 2 × 22 = 44.

Teacher's Note:
1. In 12 hours the hands coincide 11 times, are opposite 11 times and are at right angles 22 times.
2. Double the 12-hour count to get the count for a full day.

Answer: (d) 22

Explanation:
1. The hands are opposite (180° apart) once every hour, but between 5 and 7 it happens only once, at 6 o'clock.
2. So it happens 11 times in 12 hours, and 11 × 2 = 22 times in a day.

Teacher's Note:
1. In 12 hours the hands coincide 11 times, are opposite 11 times and are at right angles 22 times.
2. Double the 12-hour count to get the count for a full day.

Answer: (b) 15°

Explanation:
1. Angle = |30H − 5.5M| with H = 6, M = 30.
2. = |180 − 165| = 15°.

Teacher's Note:
1. Use the formula angle = |30H − 5.5M|; if the result exceeds 180°, subtract it from 360°.
2. Remember the hour hand moves 0.5° per minute, so it is never exactly on the hour mark except at full hours.

Answer: (d) 27³/₁₁ minutes past 5

Explanation:
1. At 5 o'clock the minute hand is 25 minute spaces behind the hour hand.
2. It gains 55 minute spaces in 60 minutes, so it needs 25 × 60/55 = 300/11 minutes.
3. 300/11 = 27³/₁₁ minutes past 5.

Teacher's Note:
1. The minute hand gains 5.5° (or 11/12 of a minute space) on the hour hand every minute.
2. Write the required angle as an extra gain (or loss) over the starting angle at H o'clock and divide by 5.5.

Answer: (d) 15°

Explanation:
1. Angle = |30H − 5.5M| with H = 5, M = 30.
2. = |150 − 165| = 15°.

Teacher's Note:
1. Use the formula angle = |30H − 5.5M|; if the result exceeds 180°, subtract it from 360°.
2. Remember the hour hand moves 0.5° per minute, so it is never exactly on the hour mark except at full hours.

Answer: (b) 43⁷/₁₁ minutes past 5

Explanation:
1. At 5 o'clock the hands are 25 minute spaces apart. To be at right angles after 5:30, the minute hand must get 15 spaces ahead, i.e. gain 25 + 15 = 40 spaces.
2. It gains 55 spaces in 60 minutes, so time = 40 × 60/55 = 480/11 minutes.
3. 480/11 = 43⁷/₁₁ minutes past 5.

Teacher's Note:
1. The minute hand gains 5.5° (or 11/12 of a minute space) on the hour hand every minute.
2. Write the required angle as an extra gain (or loss) over the starting angle at H o'clock and divide by 5.5.

Answer: (b) 49¹/₁₁ minutes past 9

Explanation:
1. The hands coincide when 5.5M = 30H, i.e. M = 60H/11.
2. With H = 9: M = 540/11 = 49¹/₁₁ minutes past 9.

Teacher's Note:
1. The minute hand gains 5.5° (or 11/12 of a minute space) on the hour hand every minute.
2. Write the required angle as an extra gain (or loss) over the starting angle at H o'clock and divide by 5.5.

Answer: (d) 5 hours 15 minutes

Explanation:
1. Mirror time = 12:00 − actual time (written as 11:60 to subtract easily).
2. 11:60 − 6:45 = 5:15.

Teacher's Note:
1. Actual time and mirror time together always make 12:00.
2. Write 12:00 as 11:60 to avoid borrowing errors.

Answer: (b) 10°

Explanation:
1. The hour hand turns 360° in 12 hours = 720 minutes, i.e. 0.5° per minute.
2. In 20 minutes it turns 20 × 0.5 = 10°.

Teacher's Note:
1. Hour hand: 0.5° per minute (30° per hour).
2. Minute hand: 6° per minute; second hand: 6° per second.

Answer: (d) 3°

Explanation:
1. The second hand covers 360° in 60 seconds, so 180° takes 30 seconds.
2. The minute hand moves 6° per minute, so in 30 seconds (half a minute) it moves 3°.

Teacher's Note:
1. The second hand is 60 times as fast as the minute hand.
2. So divide the second hand's angle by 60: 180° ÷ 60 = 3°.

Answer: (d) Both (a) and (c)

Explanation:
1. At 5 o'clock the angle is 150°. The angle becomes 30° when it changes by 120° (before the hands meet) or by 180° (after the minute hand passes).
2. 120 ÷ 5.5 = 240/11 = 21⁹/₁₁ minutes; 180 ÷ 5.5 = 360/11 = 32⁸/₁₁ minutes.
3. Both times lie between 5 and 6, so both (a) and (c) are correct.

Teacher's Note:
1. The minute hand gains 5.5° (or 11/12 of a minute space) on the hour hand every minute.
2. Write the required angle as an extra gain (or loss) over the starting angle at H o'clock and divide by 5.5.

Answer: (d) 4.32 pm

Explanation:
1. From 8 a.m. to 4 p.m. next day the clock shows 32 hours passing.
2. The clock runs 24 h − 24 min = 23 h 36 min = 23.6 hours for every 24 correct hours.
3. Correct time elapsed = 32 × 24/23.6 = 1920/59 h ≈ 32 h 32.5 min.
4. So the right time is about 4.32 pm.

Teacher's Note:
1. For a slow clock, correct time = clock time × (24 h) ÷ (hours shown by the clock in 24 correct hours).
2. Always count the elapsed clock time first, then convert it.

Answer: (b) 2 p.m. on Wednesday

Explanation:
1. Time from Monday noon to 2 p.m. next Monday = 7 days 2 hours = 170 hours.
2. Total gain = 2 min + 4 min 48 s = 6.8 minutes in 170 hours.
3. To gain 2 minutes it needs 170 × 2/6.8 = 50 hours = 2 days 2 hours.
4. Monday noon + 50 hours = 2 p.m. on Wednesday.

Teacher's Note:
1. For a clock that gains or loses uniformly, the error changes in direct proportion to time elapsed.
2. Add the 'slow' amount and the 'fast' amount to get the total change, then find when the change equals the initial error.

Answer: (b) Gains 56⁸/₇₇ minutes

Explanation:
1. Correct hands coincide every 720/11 = 65⁵/₁₁ minutes. Here the gap is 63 minutes, which is shorter, so the clock gains.
2. Gain in 63 minutes = 720/11 − 63 = 27/11 minutes.
3. Gain per day = (27/11) × (1440/63) = 4320/77 = 56⁸/₇₇ minutes.

Teacher's Note:
1. Correct hands coincide every 65 5/11 minutes; a shorter gap means the clock gains, a longer gap means it loses.
2. Gain or loss per day = (65 5/11 − gap) ÷ gap × 1440 minutes.

Answer: (b) 2.15 pm on 4th

Explanation:
1. Time from 9 a.m. on 3rd to 3 p.m. on 6th = 3 days 6 hours = 78 hours.
2. Total loss = 15 + 25 = 40 minutes in 78 hours.
3. To lose the first 15 minutes it needs 78 × 15/40 = 29.25 hours = 29 h 15 min.
4. 9 a.m. on 3rd + 29 h 15 min = 2.15 p.m. on 4th.

Teacher's Note:
1. For a clock that gains or loses uniformly, the error changes in direct proportion to time elapsed.
2. Add the 'slow' amount and the 'fast' amount to get the total change, then find when the change equals the initial error.

Answer: (d) 30 minutes

Explanation:
1. Every hour the clocks move apart by 3 + 2 = 5 minutes.
2. From 10 a.m. to 4 p.m. is 6 hours, so the difference = 6 × 5 = 30 minutes.

Teacher's Note:
1. When one clock gains and the other loses, add their rates to get the rate of separation.
2. If both gain (or both lose), subtract the rates instead.

Answer: (d) 12 am on Wednesday

Explanation:
1. Time from Sunday noon to 4 p.m. next Sunday = 7 days 4 hours = 172 hours.
2. Total gain = 3 min + 5 min 36 s = 8.6 minutes in 172 hours.
3. To gain 3 minutes it needs 172 × 3/8.6 = 60 hours = 2 days 12 hours.
4. Sunday noon + 60 hours = midnight, i.e. 12 am at the start of Wednesday.

Teacher's Note:
1. For a clock that gains or loses uniformly, the error changes in direct proportion to time elapsed.
2. Add the 'slow' amount and the 'fast' amount to get the total change, then find when the change equals the initial error.

Answer: (d) 180°

Explanation:
1. From 8 a.m. to 2 p.m. is 6 hours.
2. The hour hand turns 30° per hour, so 6 × 30 = 180°.

Teacher's Note:
1. The hour hand turns 30° per hour and 0.5° per minute.
2. Count elapsed hours carefully across noon (8 a.m. to 2 p.m. is 6 hours).