# Clocks and Calendars Practice Set 1

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# Clocks and Calendars Practice Set 1

### Introduction

Clock Problems is all about the hour’s hand, second hand, and minutes hand. In this chapter, the problems are based mainly on the movement of the clock hands like minute spaces, minute hand, hour hand and the angles between the hands.

Calendar deals with odd days, leap year, ordinary year, counting of odd days, and day of the week related to odd days. To find the day of the week on a given date concept of odd days is used. Clocks and Calendars Practice Set 1 Presents most important questions related to Clocks and Calendars.

### Quiz

Q1. At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions.

A. 3:49
B. 3:15
C. 3:39 $$\frac {1}{11}$$
D. 3:49 $$\frac {1}{11}$$

Elplanation:
On straight line means 180 degree angle

180= $$\frac {11}{{2}{m}} – 30 h$$

180= $$\frac {11}{{2}{m}} – 30 \times 3$$

180= $$\frac {11}{{2}{m}} – 90$$

(180 + 90) 2 = 11 m

m = $$\frac {540}{11} = 49 \frac {1}{4}$$

Q2. At what time, between 3 o’clock and 4 o’clock, both the hour hand and minute hand coincide each other?

A. 3:30
B. 3:16 $$\frac {4}{11}$$
C. 3:16 $$\frac {11}{4}$$
D. 3:16 $$\frac {7}{11}$$

Explanation:
Coincide means 00 angle.

0 = $$\frac {11}{2} m – 30 \times 3$$

11 m = $$\times 2$$ = 180

m = 90 $$\times 2$$ = 180

$$\frac {180}{11} = 16 \times \frac {4}{11}$$

So, Time = 3 : 16 $$\frac {4}{11}$$

Q3. How many years have 29 days in February from 2001 to 2100.

A. 26
B. 25
C. 23
D. 24

Elplanation:
100th year is not a leap year. So 24 February’s has 29 days

Q4. 2012 January 1st is Sunday, then which day is the Indian Independence day of the same year.

A. Saturday
B. Wednesday
C. Thursday
D. Friday

Elplanation:
30 + 29 + 31 + 30 + 31 + 30 + 31 + 15 = 227/7 = reminder = 3

So Independence day is Wednesday

Q5. Which year has the same calendar as 1700 ?

A. 1705
B. 1706
C. 1707
D. 1708

Elplanation:

 Year: 1700 1701 1702 1703 1704 1705 Odd Days: 1 1 1 1 2 1

Q1. If Arun’s birthday is on May 25 which is Monday and his sister’s birthday is on July 13. Which day of the week is his sister’s birthday?

A. Monday
B. Wednesday
C. Thursday
D. Friday

Elplanation:
Reference day : May 25th Monday

Days from May 25th to July 13 = 6 + 30 + 13 = 49

No of Odd Days : $$\frac {49}{7}$$ = 0

Q2. March 1st is Wednesday. Which month of the same year starts with the same day?

A. October
B. November
C. December
D. None of these

Elplanation:

 Month: Mar April May June July Aug Sep. Oct. Odd Days: 3 2 3 2 3 3 2 3

Total 21 odd days. $$\frac {21}{7}$$ = 0. So November has start with the same day.

Q3. How many times does the 29th days of the month occur in 400 consecutive years

A. 97 times
B. 4400 times
C. 4497 times
D. none

Elplanation:
In 400 consecutive years there are 97 leap years. Hence in 400 consecutive years, February has the 29th day 97 times, and the remaining 11 months have the 29th day 400 x 11 or 4400 times.

Therefore, 29th day of the month occurs (4400 + 97) or 4497 times

Q4. Given that on 10th November 1981 is Tuesday, what was the day on 10th November 1581

A. Monday
B. Thursday
C. Sunday
D. Tuesday

Elplanation:
After every 400 years, the same day comes.

Thus if 10th November1981 was Tuesday, before 400 years i.e on 10th November 1581, it has to be Tuesday.

Q5. The angle bounded by the hands of a clock at 3:30 is

A. 60°
B. 45°
C. 75°
D. 90°

Elplanation:
Required angle = $${90}^{0} – 30 \times \frac {1}{{2}^{0}}$$

Q1. The hour and the minute hands of a clock coincide at midnight. At what time of the day will the hands coincide again?

A. 1 – 06 O’ Clock
B. 1 – 05 $$\frac {5}{11}$$ O’ Clock
C. 1 – 05 O’ Clock
D. 1 – 06 $$\frac {4}{11}$$ O’ Clock

Elplanation:
If both the hands start moving together from the same position they will coincide after 65$$\frac {5}{11}$$ minutes

Q2. After 12 noon the first right angle will be formed between the hands of a clock at

A. 3 p.m.
B. 3.16 p.m.
C. 2.52 p.m.
D. 2.40 p.m.

Elplanation:
The minute hand gains 5 $$\frac {{1}^{0}}{2}$$ over the hour hand in one minute.

therefore, $${90}^{0}$$ are gained in $$\frac {90}{5 \frac {1}{2}}$$ min

Q3. Two clocks are set correctly at 10 a.m. on Friday. The first clock gains two minutes every hour, which is twice as much as the second. What time will be the second clock register when the correct time is 2 p.m. on the following Monday?

A. 3.22 p.m.
B. 3.16 p.m.
C. 2.52 p.m.
D. 2.40 p.m.

Elplanation:
The second clock gains(24 + 24 + 24 + 4 minutes)

Q4. At how many minutes past 5 p.m. are the hands of a clock at right angles to one another between 5 p.m. and 6 p.m.?

A. 10 $$\frac {10}{11}$$ min and 43 $$\frac {7}{11}$$
B. 10 $$\frac {1}{11}$$ min and 43 $$\frac {4}{11}$$
C. 10 min and 40 min
D. None of these

Elplanation:
The hands of the clock will be at right angels after 5 p.m. once the minute hands has traversed 150° + 90°=240° over the minute hand.

Note that 330° is gained in 60 minutes.

Q5. How much does a watch gain or lose per day if its hands coincide every 64 minutes of the correct time?

A. Loses 90 minutes
B. Gains 90 minutes
C. Loses 32 $$\frac {8}{11}$$ minutes
D. Gains 32 $$\frac {8}{11}$$ minutes

Elplanation:
in a correct watch, the minute hand gains 60 minutes over the hour hand (i.e. coincident) in 65 $$\frac {5}{11}$$ minutes.

### Exams

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