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Applied Maths Chapter 3 Solutions
Quantitative Aptitude
EXERCISE- 3.5
Q.1 Workout for the day of the week on the given date
(i) 4th January 2002
(ii) 13th August 1975
Ans. (i) No. of odd days:
From 0 – 2000 = 0 odd day
Now, 1st January 2001 – 31st December 2001 = 1 odd day
1st January 2002 – 4th January 2002 = 4 odd days
Total no. of odd days = 5
Therefore, 5th day will be Friday
(ii) No. of odd days:
From 0 – 1600 = 0 odd day
From 1600 – 1900 = 1 odd day
Now,
From 1st January 1901 to 1974 = 18 x 2 + 56 = 36 + 56 = 92
From January 1975 to 13th August 1975 = 31 + 28 + 31 + 30 + 31 + 30 + 31 + 13 = 225
Total no. of days = 0 + 1 + 92 + 225 = 318
Dividing 318 with 7 = 7 x 45 + 3
= 3 odd days
Therefore, the Day on 13th August 1975 will be Wednesday.
Q.2 Workout for the day of the week on the given date:
(i) 22nd November 2025
(ii) 21st September 2080
Ans. (i) No. of odd days:
From 0 – 2000 = 0 odd day
From 2001 – 2024 = 6 x 2 + 18 x 1
= 12 + 18 = 30 odd days
[6 Leap year + 18 non leap year]
Now, 1st January 2005 – 22nd November 2025
= 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 22
= 326 odd days
Total no. of odd days = 0 + 30 + 326 = 356
Dividing 356 with 7 = 7 x 50 + 6
= 6 odd days
Therefore, 6th day will be Saturday
(ii) No. of odd days:
From 0 – 2000 = 0 odd day
From 2001 – 2079 = 19 x 2 + 60 x 1
= 38 + 60 = 98 odd days
[19 Leap year + 60 non leap year]
Now, 1st January 2080 – 21st September 2080
= 31 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 21 = 265 odd days
Total no. of odd days = 0 + 98 + 265 = 363
Dividing 363 with 7 = 7 x 51 + 6
= 6 odd days
Therefore, 6th day will be Saturday
Q.3 If today is a Tuesday, what will be the day on the 7706th day?
Ans. Given that, today is Tuesday
To find odd days we have to divide 7706 with 7
Therefore, the remainder (odd days) = 6
Hence, the 7706th day will be Monday which is 6 days after Tuesday.
Q.4 If 22 April 1970 was Wednesday, what would be the day on 31 May 1999?
Ans. Given that 22 April 1970 was Wednesday,
From 23 April 1970 to 22 April 1999
(Here comes, 7 leap years + 22 Non – leap years)
So, No. of odd days = 7 x 2 + 22 x 1 = 14 + 22 = 36 days
Now, From 23 April to 31st May 1999 = 8 + 31 = 39
Total no. of odd days = 36 + 39
= 75
Dividing 75 with 7 = 7 x 10 + 5
Therefore, After 5 days it will be Monday.
Q.5 If 10 June 1948 was Thursday, what would be the day on 16 November 1969?
Ans. Given that 10 June 1948 was Thursday,
From 10 June 1948 to 10 June 1969
(Here comes, 5 leap years + 16 Non – leap years)
So, No. of odd days = 5 x 2 + 16 x 1
= 10 + 16
= 26 days
Dividing 26 with 7 = 7 x 3 + 5
Therefore, no. of odd days = 5 days
Now, From 11th June 1969 to 6th November1969
20 + 31 + 31 + 30 + 31 + 16 = 159
Dividing 159 with 7 = 7 x 22 + 5
Therefore, no. of odd days = 5 days
Total no. of odd days = 5 + 5
= 10
Dividing 10 with 7 = 7 x 1 + 3
Therefore, After 3 days it will be Sunday.
Q.6 If 8 March 1996 was Friday, what was the day on 8 March 1993?
Ans. No. of odd days:
From 8th March 1993 to 7th March 1994 = 1
From 8th March 1994 to 7th March 1995 = 1
From 8th March 1995 to 7th March 1996 = 2 [Leap year]
Total no. of odd days = 4
Therefore, 4 days before Friday was Monday.
Q.7 Thursday fell on which date of April 2007?
Ans. No. of odd days:
From 0 – 2000 = 0 days
From 2001 – 2006 = 1 x 2 + 5 x 1
= 2 + 5 = 7
Dividing 7 with 7 = 0 odd days
(1 leap year + 5 nonleap years)
Now,
From 1st January 2007 to 31st March 2007 = 31 + 28 + 31 = 90
Dividing 90 with 7 = 7 x 12 + 6
= 6 odd days
Therefore, On 1st April will be Sunday
2nd April will be Monday
3rd April will be Tuesday
4th of April will be Wednesday
5th April will be Thursday
So, Thursday fell on dates of April will be 5th, 12th, 19th, 26th
Q.8 Saturday fell on which date in May 1999?
Ans. No. of odd days:
From 0 -1600 = 0
From 1600 – 1900 = 1
From 1901 – 1998 = 24 x 2 +75 x 1
= 48 + 75 = 123
Dividing 123 with 7 = 7 x 17 + 4
= 4 odd days
(24 leap year + 75 non leap year)
Now,
January 1999 = 31 days
February 1999 = 28 days
March 1999 = 31 days
April 1999 = 30 days
Total no. of odd days = 0 + 1 + 4 + 1 = 6 odd days
Therefore, 1st May = Saturday
So, Saturday fell on dates of May will be 8th, 15th, 22nd, 29th
Q.9 Rahul’s birthday is on Saturday 5th June. On what day of the week will be Radhika’s birthday in the same year, if Radhika was born on 13th September?
Ans. Given that, Rahul’s birthday is on Saturday 5th June
So, 6th June = 25 days
July = 31 days
August = 31 days
September = 30 days
Total no. of days = 100
Dividing 100 with 7 = 7 x 14 + 2
= 2 odd days
So, After 2 days of Saturday, there will be Monday
Therefore, Radhika’s birthday will be on Monday.
Q.10 The Indian government has announced a complete lockdown for the entire country from the midnight of 25th March 2020 till the midnight of 14th April 2020 due to diseases COVID-19 outbreak. But keeping in view the grim situation the lockdown was further extended till 3rd May 2020.
(i) Calculate the total number of days for which the lockdown lasted.
(ii) If 25th March 2020 is Wednesday, then find which day of the week will fall on 3rd May 2020.
Ans. (i) No. of days in March = 6 days
No. of days in April = 30 days
No. of days in May = 3 days
Total no. of days = 39
Dividing 39 with 7 = 7 x 5 + 4
= 4 odd days
(ii) Given that, the 25th March is Wednesday
So, after 4 days it will be Sunday
Therefore, Sunday is the day on 3rd May.
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 Applied Maths Chapter 3
In 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, Applied Maths Chapter 3 promises an enriching learning experience that will set you on the path to success. Applied Maths Chapter 3, we delve deep into advanced mathematical concepts that are crucial for understanding.
