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Class 11 Applied Maths Chapter 3 Solutions
Quantitative Aptitude
EXERCISE- 3.3
Q.1 At what time do the hands of the clock meet between 4:00 and 5:00?
Ans. At 4’o clock, the hour hand is at 4 and the minute hand is at 12. It means the angle between the two hands of the clock is 120°.
To catch the hour hand, the minute has to cover a relative distance of 120° at a relative speed of 5.5° per minute.
Therefore,
The time required to coincide the hands = 120/5.5 min
= (120 x 10)/55
= (120 x 2)/11
= 240/11
= 21 9/11
= 21 min 9/11 x 60 sec
= 21 min 49 sec
= 4 : 21: 49
Q.2 At what time between 7:00 and 8: 00 will the hands of a clock coincide?
Ans. At 7’o clock, the hour hand is at 7 and the minute hand is at 12. It means the angle between the two hands of the clock is 210°.
To catch the hour hand, the minute has to cover a relative distance of 210° at a relative speed of 5.5° per minute.
Therefore,
The time required to coincide the hands = 210/5.5 min
= (210 x 10)/55
= (210 x 2)/11
= 420/11
= 38 2/11
= 38 min 2/11 x 60 sec
= 38 min 11 sec
= 7 : 38: 11
Q.3 At what time between 8:00 and 9: 00 will the hands of the clock be at right angles?
Ans. If min hand at 12
Then the angle is turned when it reaches 5 = 150°
Relative gain = 5.5
Therefore, 150°/5.5 = (150 x 10)/5.5
150°/5.5 = 300/11
= 27 3/11
= 27 min 3/11 x 60 sec
= 27 min 1 sec
Therefore, Time = 8: 27: 16
Q.4 At what time between 5:00 and 6: 00 will the hands of the clock be at right angles?
Ans.
Distance = 150° – 90° = 60°
Relative Distance = 11/2 = 5.5
Time = 60°/(11/2)
= 120°/11
= 10.9
= 10 min 54 sec
Distance = 60° + 180° = 120°
Relative angle = 11/2
Time = 240/(11/2)
= 480/11
= 43.63
= 43 min 38 sec
Therefore, Time = 5: 43: 38
Q.5 Find the acute angle between two hands of a clock at 10: 10 a.m.
Ans. At 10: 00 a.m., the Angle between the two hands of the clock = 60°
Relative gain in 1 min = 5.5
Relative gain in 10 min = 5.5 x 10
= 55°
Total angle = 60 + 55
= 115°
Q.6 Find the angle between two hands of a clock at 4: 20 p.m.
Ans. H = 4, M = 20
So, the angle between the two hands of the clock at 4: 20
A = |30 H – 11/2 M|
= 30 x 4 – 11/2 x 20|
= |120 – 110|
= 10°
Q.7 At what time between 4’0 clock and 5’0 clock will the hands of a clock make an angle of 20°?
Ans. H = 4, A = 20
As we know,
A = |30H – 11/2 M|
20° = |30 x 4 – 11/2 M|
20° = |120 – 11/2 M|
±20 = 120 – 11/2 M
Taking the -ve sign, we have
-20 = 120 – 11/2 M
11/2 M = 120 + 20
11/2 M = 140
M = 280/11
M = 25 5/11
= 25 Min (5 x 60)/11 sec
= 25 min 27 sec
Therefore, Time = 4: 25: 27
Taking the +ve sign, we have
20 = 120 – 11/2 M
11/2 M = 120 – 20
11/2 M = 100
M = 200/11
M = 18 2/11
= 18 Min (2 x 60)/11 sec
= 18 min 11 sec
Therefore, Time = 4: 18: 11
Q.8 Find the angle between the hands of a clock when it struck 15 minutes past 7.
Ans. H = 7, M = 15
As we know,
A = |30 x 7 – 11/2 x 15|
= |210 – 165/2|
= |120 – 82.5|
= 127.5
Therefore, the Angle between the hand of a clock = 127.5°
Q.9 By 20 minutes past 5, how many degrees has the hour-hand turned through?
Ans. Angle turned by hour hand in 1 min = 0.5°
Angle turned by hour hand in 20 min = 0.5 x 20
= 10.0
= 10°
Q.10 A watch gains 5 seconds in 3 minutes and was set right at 10:00 a.m. What time will it show at 10:00 p.m. on the same day?
Ans. Time gain in 3 min = 5 sec
Time gain in 60 min = 20 x 5
= 100 sec
Time gain in 1 hour = 100 sec
Therefore,
Time gain in 12 hour = 12 x 100
= 1200 min
1200 sec = 1200/60 min
= 20 min
So, the time shown at 10:00 P.M will be = 10: 20 P.M
Q.11 A watch gains 3 minutes in 1 hour and was set right at 8:00 a.m. What time will it show at 9:30 p.m. on the same day?
Ans.
Q.12 A clock loses 5 seconds in 1 minute and was set right at 7:00 a.m. What time will it show 3:00 p.m. on the same day?
Ans. Time loses in 1 min = 5 sec
Time loses in 60 min = 60 x 5
= 300 sec
Time loses in 1 hour = 300 sec
Therefore,
Time loses in 8 hour = 8 x 300
= 2400 min
2400 sec = 2400/60 min
= 40 min
So, the time shown at 3:00 P.M will be = 2: 40 P.M
Q.13 A watch loses 5 minutes in 2 hours and was set right at 6:00 a.m. What time will it show 6:00 a.m. the next day?
Ans. Given that time lost in 2 hours = 5 min
Now, according to the question, the clock has moved 24 hrs
Therefore, loss in 24 hours would be,
Q.14 A watch gains 5 seconds in 3 minutes and was set right at 7 a.m. If it shows 4: 15 in the afternoon on the same day. What is the correct time?
Ans. Total Time = 9 hours 15 min
= 9 x 60 + 15
= 540 + 15 = 555 min
ATQ, 5 sec gain in 3 min
5 x 12 gain in 3 x 12
60 sec gain in 36 min
1 min gain in 36 min
Incorrect clock moves 37 min in 36 min
The incorrect clock moves 1 min = 36/37 min
Incorrect clock moves in 555min = 36/37 x 555 min = 540/60
= 9 hours
The correct Time will be 4: 00 p.m
Q.15 A watch loses 3 seconds in 2 minutes and was set right at 8:00 a.m. If it shows 9:00 in the evening on the same day, what is the correct time?
Ans. No. of hours = 13 hours
= 780 min
ATQ, 3 sec loss in 2 min
3 x 20 loss in 2 x 20
1 min loss in 40 min
Incorrect clock moves 39 min in 40 min
The incorrect clock moves 1 min = 40/39 min
Incorrect clocks move in 780 min = 40/39 x 780 = 800 min
= 800/60 = 13.3333 hours
The correct Time will be 9: 20 p.m
Q.16 A watch loses 6 minutes every hour and was set right at 11:00 a.m. on a Monday. When will it show the correct time again?
Ans. 6 min loses in 1 hour
6 x 10 min loses in 10 hours
1-hour loss in 10 hours
12 hours loses in 120 hours
No. of days = 120/24hrs
= 5 days
Therefore, Saturday is the day, when the correct time is shown again.
Q.17 A local train from Mumbai leaves every 40 minutes from the station. When inquired by a passenger, the help desk execution informed that the train had already left 10 minutes ago.
If this information was given at 10: 15 a.m.:
(i) At what time did the train leave the station?
(ii) At what time will the next train leave the station?
(iii) For how long will that man have to wait for the next train?
(iv) Find the angle formed between the minute hand and the hour hand when the passenger will board the next train.
Ans. (i) Given, information was given at 10: 15
ATQ, the train had left 10 minutes ago,
Therefore, the time of train leaves the station = is 10: 05
(ii) As we know, the first train leaves at 10: 05
ATQ, the train leaves after every 40 min
Therefore, time for the next train to leave the station = 10: 45
(iii) Given, Information asked at 10: 15
And the time for the next train is 10: 45
Therefore, A man has to wait for 30 minutes.
(iv) The time for the next train is 10: 45
So, H = 10, M = 45
A = 30H – 11/2M
= 30 x 10 – 11/2 x 45
= 300 – 495/2
= 300 – 247.5
= 52.5°
FAQ’s related to Applied Maths Chapter 3 on Quantitative Aptitude:
Q.1 Why is Quantitative Aptitude important?
Ans. Quantitative aptitude skills are crucial for various competitive exams, entrance tests, and job interviews. They are also essential for everyday tasks such as budgeting, financial planning, and decision-making.
Q.2 What topics are covered in Applied Maths Chapter 3?
Ans. Applied Maths Chapter 3 on Quantitative Aptitude typically covers topics such as percentages, profit and loss, clock, time and distance, time and work, averages, ratio and proportion, etc.
Q.3 How will mastering Chapter 3 help you in future exams?
Ans. Mastering Chapter 3 will provide you with a strong foundation in quantitative aptitude, which is essential for scoring well in various competitive exams such as GRE, GMAT, SAT, CAT, banking exams, etc. These exams often contain sections dedicated to quantitative aptitude, and a good score in these sections can significantly enhance your overall performance.
These are few Frequently Asked Questions relating to Class 11 Applied Maths Chapter 3
In Class 11 Applied Maths chapter 3, you will explore fascinating topics that form the backbone of practical problem-solving techniques. Through clear explanations, illustrative examples, and step-by-step solutions, you’ll grasp complex concepts effortlessly. Whether you’re preparing for exams or simply eager to deepen your mathematical understanding, Class 11 Applied Maths Chapter 3 promises an enriching learning experience that will set you on the path to success. Class 11 Applied Maths Chapter 3, we delve deep into advanced mathematical concepts that are crucial for understanding.
Class 11 Applied Maths Chapter 3 EXCERCISES: