a. 25 | 1 | minutes before 3 pm |

11 |

b. 38 | 7 | minutes before 3 pm |

11 |

c. 43 | 7 | minutes past 2 pm |

11 |

d. 50 | 5 | minutes past 2 pm |

11 |

Answer: c. 43 | 7 | minutes past 2 pm |

11 |

Tip:

In one hour, MINUTE hand travels 60 minutes

HOUR hand travels just 5 minute spaces

Thus,

MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60

At 2pm hour hand and minute hand difference = 10 minutes

So to be in straight line and opposite direction between 2 and 3, minute hand must be 30 minutes ahead of the hour hand

For 30 minutes ahead, minute hand must travel (30 + 10) = 40 minutes more

In 60 minutes, minute hand gains 55 min.

In ? minutes it gains 40 minutes

∴ ? = | 40 x 60 | = 43 | 7 | minutes past 2 pm |

55 | 11 |

a. 43 | 9 | minutes past 10 o' clock and 3 | 3 | minutes past 11 o' clock |

11 | 11 |

b. 43 | 9 | minutes past 10 o' clock and 58 | 9 | minutes before 11 o' clock |

11 | 11 |

c. 43 | 9 | minutes past 10 o' clock and 3 | 3 | minutes before 11 o' clock |

11 | 11 |

d. 3 | 3 | minutes before 11 o' clock and 63 | 3 | minutes past 10 o' clock |

11 | 11 |

Answer: c. 43 | 9 | minutes past 10 o' clock and 3 | 3 | minutes before 11 o' clock |

11 | 11 |

Tip:

In one hour, MINUTE hand travels 60 minutes

HOUR hand travels just 5 minute spaces

Thus,

MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60 minutes

At 10 o'clock hour hand & minute hand difference = 50 minutes.

So to be 8 min apart, minute hand must be at (50 - 8 =) 42 minutes or (50 + 8 =) 58 minute s position

For 42 minutes, minute hand must travel 42 minutes more

In 60 minutes, minute hand gains 55 min.

In ? minutes it gains 42 minutes

∴ ? = | 42 x 60 | = 43 | 9 | minutes past 10 o' clock |

55 | 11 |

In 60 minutes, minute hand gains 55 min.

In ? minutes it gains 58 minutes

∴ ? = | 58 x 60 | = 63 | 3 | minutes past 10 o' clock = 1 hour + 3 | 3 | minutes |

55 | 11 | 11 |

That means 3 | 3 | minutes past 11 o' clock |

11 |

a. 56 | 65 | minutes Loss |

11 |

b. 66 | 5 | minutes Loss |

11 |

c. 72 | 7 | minutes Gain |

11 |

d. 78 | 74 | minutes Gain |

11 |

Answer: d. 78 | 74 | minutes Gain |

11 |

Tip:

In one hour, MINUTE hand travels 60 minutes

HOUR hand travels just 5 minute spaces

Thus,

MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60 minutes

If the minute hand wants to meet the hour hand, it can meet only after it travels 60 minutes.

So,

In 60 minutes, minute hand gains 55 min.

In ? minutes it gains 60 minutes

∴ ? = | 60 x 60 | = 65 | 5 | minutes = Minute and hour hand meet after these many minutes |

55 | 11 |

Hands meet after 62 minutes i.e. earlier

So the clock gains (65 | 5 | - 62) = | 38 | minutes |

11 | 11 |

So in 62 minutes clock gains | 38 | minutes |

11 |

? minutes = | 38 | x | (24 x 60 minutes) | = | 6080 | = 78 | 74 | minutes |

11 | 63 minutes | 77 | 11 |

a. At 3 pm

b. At 9 pm

c. At 29 | 8 | minutes before 10 pm |

11 |

d. At 32 | 8 | minutes past 9 pm |

11 |

Answer: d. At 32 | 8 | minutes past 9 pm |

11 |

Tip:

In one hour, MINUTE hand travels 60 minutes

HOUR hand travels just 5 minute spaces

Thus,

MINUTE hand gains (60 - 5) = 55 minutes over HOUR hand in 60

At 9 pm hour hand and minute hand difference = 45 minutes

They already are at right angle. We want after 9 pm.

For right angle, minute hand must be 15 minutes behind

For 15 minutes behind, minute hand must travel (45 - 15) = 30 minutes more

In 60 minutes, minute hand gains 55 min.

In ? minutes it gains 30 minutes

∴ ? = | 30 x 60 | = 32 | 8 | minutes past 9 pm |

55 | 11 |

a. 28 minutes 20 seconds before 10 am

b. 31 minutes 40 seconds past 10 am

c. 28 minutes 20 seconds past 11 am

d. 31 minutes 40 seconds past 11 am

**Answer:** b. 31 minutes 40 seconds past 10 am

**Explanation:**

From 1.00 am Sunday to 11 am Monday we have

24 hours (till 1 am Mon) + 10 hours = 34 hours

20 minutes gained in 24 hours

∴ ? minutes gained in 34 hours

∴ ? = 28.333 minutes = 28 minutes 20 seconds

Alarm will go off at 11 am

But actual time will be less than that because clock had gained time.

**∴ Actual time =** 11am - 28 minutes 20 seconds **= 31 minutes 40 seconds past 10 am.**