Calendar Problems in Reasoning: 20 Unique Questions with Solutions

The calendar is an essential topic in logical reasoning, especially for competitive exams like SSC CGL, Banking, and UPSC. It includes questions related to finding the day of the week, leap years, odd days, and other calendar-based problems. In this blog, we will explore 20 unique calendar problems with detailed explanations to help you master this topic.

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1. Finding the Day of a Given Date

Question: What was the day of the week on 15th August 1947?

Solution:

• Base year: 1900 (1st Jan 1900 was a Monday)

• Counting odd days:

  • 1900-1947 = 47 years (11 leap years + 36 normal years) → (11×2 + 36×1) = 58 odd days → 58 ÷ 7 = 2 odd days

  • January to August 15th, 1947 → 3 + 0 + 3 + 2 + 3 + 2 + 3 + 5 = 21 odd days → 21 ÷ 7 = 0 odd days

  • Total odd days = 2

  • Monday + 2 days = Friday

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2. Leap Year Identification

Question: Which of the following is a leap year? A) 1700
B) 1800
C) 1900
D) 2000

Solution: A year is a leap year if it is divisible by 4, but if it is a century year, it must be divisible by 400. Only 2000 is a leap year.

Answer: D) 2000

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3. Finding Odd Days

Question: How many odd days are there in 400 years?

Solution:

• 1 normal year = 365 days = 1 odd day

• 1 leap year = 366 days = 2 odd days

• 400 years = 100 leap years + 300 normal years

• Odd days = (100×2 + 300×1) = 200 + 300 = 500 days

• 500 ÷ 7 = 0 odd days

Answer: 0 odd days

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4. Next Same Calendar Year

Question: When will the calendar of 2024 repeat?

Solution:

• Leap years repeat after 28 years.

• The next year with the same calendar as 2024 will be 2052.

Answer: 2052

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5. Previous Same Calendar Year

Question: Which year had the same calendar as 2023?

Solution:

• Normal years repeat after 6 or 11 years.

• The last same calendar was in 2017.

Answer: 2017

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6. First Day of Any Century

Question: What is the first day of the 21st century (1st January 2001)?

Solution:

• 1st Jan 1901 was Tuesday.

• 100 years = 0 odd days.

• So, 1st Jan 2001 is also Monday.

Answer: Monday

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7. Day Calculation with Odd Days

Question: If today is Wednesday, what day will it be after 60 days?

Solution:

• 60 ÷ 7 = 4 odd days.

• Wednesday + 4 days = Sunday

Answer: Sunday

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8. Last Day of a Century

Question: What is the last day of the 20th century (31st December 2000)?

Solution:

• 31st Dec 1899 was Sunday.

• 100 years = 0 odd days.

• So, 31st Dec 2000 is also Sunday.

Answer: Sunday

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9. Repeating Calendar within a Decade

Question: When will the calendar of 2022 repeat?

Solution:

• 2022 is a normal year, and such years repeat after 6 or 11 years.

• The next similar calendar will be in 2033.

Answer: 2033

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10. Counting Fridays in a Year

Question: How many Fridays are there in a leap year?

Solution:

• 366 days = 52 weeks + 2 extra days.

• These extra days can make 53 Fridays if the year starts on a Thursday or Friday.

Answer: 52 or 53

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11. Odd Days in a Month

Question: How many odd days are there in February of a leap year?

Solution:

• February (leap year) = 29 days

• 29 ÷ 7 = 1 odd day

Answer: 1 odd day

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12. Identifying a Leap Century Year

Question: Which of the following is a leap century year? A) 1600
B) 1700
C) 1800
D) 1900

Solution: Only centuries divisible by 400 are leap years.

Answer: A) 1600

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13. Number of Sundays in a Year

Question: How many Sundays are there in a normal year?

Solution:

• 365 days = 52 weeks + 1 extra day

• Extra day can be any weekday, so Sundays remain 52 or 53.

Answer: 52 or 53

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14. Checking Leap Year

Question: Is the year 2028 a leap year?

Solution:

• 2028 ÷ 4 = yes, so it’s a leap year.

Answer: Yes

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15. 1000th Day from Today

Question: If today is Monday, what day will it be after 1000 days?

Solution:

• 1000 ÷ 7 = 6 odd days

• Monday + 6 = Sunday

Answer: Sunday

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16. Month Having Same Calendar as August

Question: Which month has the same calendar as August in a non-leap year?

Answer: February

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17. Counting Leap Years Between Two Dates

Question: How many leap years are there between 1901 and 2000?

Solution:

• Leap years: 1904, 1908, ..., 2000

• Total = 25

Answer: 25

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18. 365th Day from Today

Question: If today is Monday, what will be the day after 365 days?

Solution:

• 365 ÷ 7 = 1 odd day

• Monday + 1 = Tuesday

Answer: Tuesday

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19. Century Not a Leap Year

Question: Which of the following is not a leap year? A) 1800
B) 2000
C) 1600
D) 2400

Answer: A) 1800

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20. Calendar Repetition Rule

Question: After how many years does a leap year repeat?

Solution: 28 years.

Answer: 28 years

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These 20 questions cover all important concepts of calendar problems in reasoning. Keep practicing to master this topic!

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Clock-Based Reasoning Questions for Competitive Exams

Clock-based reasoning is a crucial topic in logical reasoning for exams like SSC CGL, Banking, Railway, and other competitive exams. These questions test a candidate’s ability to understand the movement of the clock’s hands and calculate angles, time loss or gain, mirror images, etc. Here, we present 20 unique multiple-choice questions (MCQs) along with their explanations.

Clock-Based Reasoning Questions for Competitive Exams

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1. Angle Between Hands of the Clock

Q1. What is the angle between the hands of the clock at 4:20? 

A) 100°
B) 110°
C) 120°
D) 140°

Answer: B) 110°
Explanation: Formula:
= 110°

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2. Overlapping Hands

Q2. At what time between 2:00 and 3:00 do the hour and minute hands coincide? 

A) 2:10
B) 2:20
C) 2:21.8
D) 2:30

Answer: C) 2:21.8
Explanation: The hands coincide at: minutes

= 21.8 minutes

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3. Reflex Angle Calculation

Q3. Find the reflex angle between the hands of the clock at 5:40. 

A) 100°
B) 200°
C) 220°
D) 240°

Answer: C) 220°
Explanation: Reflex angle = 360° - smaller angle
Smaller angle = 120° (using formula)
So, 220° is the reflex angle.

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4. Mirror Image of Clock Time

Q4. What will be the mirror image of 5:15? 

A) 6:45
B) 7:45
C) 6:15
D) 6:50 

Answer: A) 6:45
Explanation: Mirror image formula = 6:45

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5. Time Between Two Same Positions

Q5. How many times do the hands of the clock coincide in 12 hours? 

A) 10
B) 11
C) 12
D) 24

Answer: B) 11
Explanation: Hands coincide 11 times in 12 hours.

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6. Hands in a Straight Line

Q6. At what time between 1:00 and 2:00 do the hands of the clock form a straight line? A) 1:30
B) 1:32.73
C) 1:40
D) 1:50

Answer: B) 1:32.73
Explanation: Formula:

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7. Hands at Right Angle

Q7. At what time between 3:00 and 4:00 do the hands form a right angle? 

A) 3:15
B) 3:20
C) 3:27.3
D) 3:40

Answer: C) 3:27.3
Explanation: Formula:

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8. Fast and Slow Clocks

Q8. A clock gains 5 minutes every hour. How much will it gain in a day? 

A) 60 minutes
B) 100 minutes
C) 120 minutes
D) 150 minutes

Answer: C) 120 minutes
Explanation: 5 minutes/hour × 24 hours = 120 minutes

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9. Time Loss Calculation

Q9. A clock loses 2 minutes every 6 hours. How much time will it lose in a week? 

A) 24 minutes
B) 48 minutes
C) 56 minutes
D) 56 hours

Answer: C) 56 minutes
Explanation: 2 minutes × (24/6) × 7 days = 56 minutes

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10. Identifying Wrong Clock Time

Q10. A clock shows 9:15 but the actual time is 9:30. How much does the clock lose in a day if it continues at the same rate? 

A) 30 minutes
B) 60 minutes
C) 120 minutes
D) 150 minutes

Answer:* B) 60 minutes*
Explanation:* 15 minutes in 6 hours means 60 minutes in 24 hours.

11. Angle Between Hands of the Clock

Question: What is the angle between the hour and minute hand at 4:20?

Options:
A) 120°
B) 110°
C) 130°
D) 105°

Answer: B) 110°
Explanation: The angle formula is:

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12. Right Angle Time Calculation

Question: At what time between 3:00 and 4:00 will the hands form a right angle (90°)?

Options:
A) 3:15
B) 3:30
C) 3:40
D) 3:22

Answer: D) 3:22
Explanation: The formula for when hands are at 90°: So, the answer is 3:22.

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13. Coincidence of Hands

Question: At what time between 2:00 and 3:00 do the hands coincide?

Options:
A) 2:05
B) 2:10
C) 2:11
D) 2:12

Answer: C) 2:11
Explanation: The formula for coincidence is: So, the hands coincide at 2:11.

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14. Reflex Angle Calculation

Question: Find the reflex angle between the hands at 7:45.

Options:
A) 150°
B) 170°
C) 200°
D) 220°

Answer: D) 220°
Explanation: The smaller angle: The reflex angle = 360° - 37.5° = 220°.

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15. When Are the Hands Opposite to Each Other?

Question: At what time between 6:00 and 7:00 are the hands opposite to each other?

Options:
A) 6:40
B) 6:50
C) 6:55
D) 6:45

Answer: A) 6:40
Explanation: Hands are opposite when the angle is 180°. So, the time is 6:40.

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16. Overlapping of Hands

Question: Between 8:00 and 9:00, when will the hands overlap?

Options:
A) 8:36
B) 8:40
C) 8:43
D) 8:45

Answer: C) 8:43
Explanation: Hands overlap when: So, hands overlap at 8:43.

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17. Hands Forming 120°

Question: At what time between 5:00 and 6:00 do the hands form an angle of 120°?

Options:
A) 5:10
B) 5:20
C) 5:30
D) 5:40

Answer: B) 5:20
Explanation: So, the answer is 5:20.

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18. Hands Being 45° Apart

Question: At what time between 10:00 and 11:00 do the hands form a 45° angle?

Options:
A) 10:05
B) 10:10
C) 10:15
D) 10:20

Answer: B) 10:10
Explanation: Using the formula: So, the answer is 10:10.

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19. Angle at 12:15

Question: Find the angle between the hands at 12:15.

Options:
A) 75°
B) 90°
C) 82.5°
D) 97.5°

Answer: C) 82.5°
Explanation:

20. Clock Reflection

Question: If a clock shows 9:10, what will be its mirror image?

Options:
A) 2:50
B) 3:50
C) 3:40
D) 2:40

Answer: A) 2:50
Explanation: Mirror image formula:

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Conclusion

Clock-based reasoning is a crucial topic in SSC CGL and other competitive exams. Mastering these questions through formulas and practice will improve accuracy and speed in the exam. Keep practicing and applying these techniques to enhance your problem-solving skills!

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Seating Arrangement Questions for SSC CGL with solutions

Seating arrangement is an important topic in logical reasoning for competitive  exams like SSC CGL. These questions test a candidate’s ability to analyse and arrange people or objects according to given conditions. Below are 10 unique seating arrangement questions along with detailed explanations and solutions.

1. Circular Arrangement

Question: Six friends A, B, C, D, E, and F are sitting in a circle facing the center. B is to the immediate right of C. A is third to the left of B. E is between A and F. Who is sitting opposite to C?

Detailed Solution:

1. Since all are facing the center, the right and left directions remain the same.

2. B is to the immediate right of C, so placing them accordingly.

3. A is third to the left of B, which helps in fixing A’s position.

4. E is between A and F.

5. The final arrangement reveals that E is opposite to C.

Circular Arrangement Question

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2. Linear Arrangement (Single Row)

Question: Seven students P, Q, R, S, T, U, and V are sitting in a row facing north. Q is sitting third from the left. P is sitting at one of the extreme ends. U is sitting exactly between T and S. Who is sitting at the rightmost end?

Detailed Solution:

1. Placing Q in the third position from the left.

2. P is at one of the extreme ends.

3. U is between T and S, which helps in their positioning.

4. After arranging all, V is found at the rightmost end.

Linear Arrangement

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3. Linear Arrangement (Double Row)

Question: Eight persons are sitting in two parallel rows, facing each other. A, B, C, and D are sitting in row 1, facing south. P, Q, R, and S are sitting in row 2, facing north. C is sitting at one of the extreme ends. B is sitting second to the left of C. The person facing B is Q. Who is sitting opposite to A?

Detailed Solution:

1. Arranging row 1 with A, B, C, and D facing south.

2. Placing row 2’s persons opposite to them.

3. C is at the extreme end and B is second to the left.

4. The arrangement shows that R is opposite to A.

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4. Circular Arrangement (Facing Outwards)

Question: Five persons L, M, N, O, and P are sitting in a circle, facing outward. M is to the immediate left of O. P is second to the right of L. Who is sitting exactly between L and O?

Detailed Solution:

1. Since they are facing outward, left and right directions are reversed.

2. Placing M to the immediate left of O.

3. Placing P second to the right of L.

4. The final arrangement shows that N is between L and O.

Circular Seating Arrangement 

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5. Square Seating Arrangement

Question: Eight friends A, B, C, D, E, F, G, and H are sitting at the corners and middle of the sides of a square table. The ones sitting at the corners are facing the center, while the ones sitting at the sides are facing outward. E is sitting to the immediate right of H, who is sitting at a corner. Who is sitting opposite to H?

Detailed Solution:

1. Placing H at a corner.

2. E is to H’s immediate right.

3. Arranging others accordingly.

4. C is found sitting opposite to H.

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6. Mixed Arrangement

Question: Six persons J, K, L, M, N, and O are sitting in a row. Some are facing north while some are facing south. J is sitting at an extreme end. L is sitting second to the left of M. N is sitting to the immediate right of O, who is facing north. Who is sitting exactly in the middle?

Detailed Solution:

1. J is at an extreme end.

2. L is positioned second to the left of M.

3. N is immediately right of O.

4. M is found to be exactly in the middle.

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7. Linear Arrangement with Conditions

Question: Five people A, B, C, D, and E are sitting in a row facing north. A is sitting to the left of B but not next to C. D is sitting at an extreme end. Who is sitting second to the right of A?

Seating Arrangement Questions

Detailed Solution:

1. Placing D at an extreme end.

2. Arranging A to the left of B but not next to C.

3. The final arrangement shows that C is second to the right of A.

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8. Triangular Arrangement

Question: Seven people are sitting around a triangular table. Three sit at the corners, and four sit along the sides. P is sitting at a corner. R is sitting to the immediate right of Q. S is sitting opposite to P. Who is sitting to the left of S?

Detailed Solution:

1. Placing P at a corner.

2. R is immediately right of Q.

3. Arranging others accordingly.

4. T is found sitting to the left of S.

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9. Rectangular Seating Arrangement

Question: Ten people are sitting around a rectangular table, with four sitting at the corners and six sitting along the sides. X is sitting to the immediate left of Y. The person opposite to X is Z. Who is sitting diagonally opposite to Z?

Detailed Solution:

1. Arranging four people at corners and six along the sides.

2. X is to the left of Y.

3. Finding who sits opposite and diagonal to Z.

4. W is diagonally opposite to Z.

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10. Row Arrangement with Height Order

Question: Five boys A, B, C, D, and E are sitting in a row according to their heights. A is taller than C but shorter than B. D is shorter than C but taller than E. Who is the second tallest?

Detailed Solution:

1. Arranging them based on height order.

2. A is taller than C but shorter than B.

3. D is shorter than C but taller than E.

4. A is found to be the second tallest.

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Conclusion

Seating arrangement questions require careful reading and logical thinking. The best way to solve these is by drawing diagrams and arranging positions step by step. Regular practice will help in quick solving during exams like SSC CGL. Developing a habit of noting key points and testing different positions logically will boost confidence and accuracy in solving such questions efficiently.

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Logical Reasoning for SSC CGL: Important Questions and Explanations

 Logical reasoning is an essential part of the SSC CGL exam, testing a candidate's ability to analyze patterns, understand relationships, and solve problems efficiently. Here, we will discuss some important logical reasoning questions along with simple explanations to help you prepare effectively.

1. Number Series

Question: Find the missing number: 2, 6, 12, 20, ?, 42
Options:
A) 30
B) 28
C) 32
D) 36

Answer: B) 30
Explanation: The pattern follows +4, +6, +8, +10... So, 20 + 10 = 30

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2. Blood Relation

Question: Pointing to a boy, Rita said, "He is the son of my grandfather’s only son." How is the boy related to Rita?
Options:
A) Brother
B) Cousin
C) Nephew
D) Uncle

Answer: A) Brother
Explanation: Grandfather’s only son is Rita’s father. His son is her brother.

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3. Odd One Out

Question: Find the odd one out:
Options:
A) Apple
B) Mango
C) Potato
D) Banana

Answer: C) Potato
Explanation: All others are fruits, but potato is a vegetable.

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4. Direction Sense

Question: A man walks 10m North, turns right and walks 5m, then turns right again and walks 10m. In which direction is he now facing?
Options:
A) East
B) West
C) North
D) South

Answer: B) West
Explanation: He initially faced North, then East, then South. Now he faces West.

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5. Coding-Decoding

Question: If CAT is coded as 3120, how will DOG be coded?
Options:
A) 4150
B) 4815
C) 4740
D) 4950

Answer: C) 4740
Explanation: Each letter’s position in the alphabet is multiplied:
C (3 × 1), A (1 × 2), T (20 × 1) → 3120
D (4 × 1), O (15 × 2), G (7 × 1) → 4740

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6. Syllogism

Question: Statements:

1. All cats are animals.

2. Some animals are wild.

Conclusion:
A) Some cats are wild.
B) All animals are cats.

Options:
A) Only A follows
B) Only B follows
C) Both follow
D) None follow

Answer: D) None follow
Explanation: The given statements do not guarantee that some cats are wild or that all animals are cats.

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7. Mirror Image

Question: What will be the mirror image of 1234 in a vertical mirror?
Options:
A) 4321
B) 2143
C) 1234
D) 3412

Answer: A) 4321
Explanation: The order of digits reverses in a mirror image.

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8. Calendar Problem

Question: If 15th August 2023 was a Tuesday, what day will 15th August 2024 be?
Options:
A) Wednesday
B) Thursday
C) Friday
D) Saturday

Answer: B) Thursday
Explanation: 2024 is a leap year, so the extra day shifts it by 2 days.

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9. Puzzle-Based Question

Question: A is the father of B, but B is not the son of A. Who is B?
Options:
A) Brother
B) Daughter
C) Uncle
D) Cousin

Answer: B) Daughter
Explanation: If B is not the son, then B must be the daughter.

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10. Clock-Based Question

Question: What is the angle between the hands of the clock at 3:30?
Options:
A) 75°
B) 90°
C) 105°
D) 120°

Answer: C) 105°
Explanation: The formula is |(30×H - 5.5×M)|
= |(30×3 - 5.5×30)| = |90 - 82.5| = 105°

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Conclusion

Logical reasoning is an important section of the SSC CGL exam, and practicing different types of questions will help improve problem-solving skills. By understanding these fundamental concepts and practicing regularly, candidates can enhance their reasoning abilities and score well in the exam. Keep practicing and stay confident!

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Most Important circle Problems of Reasoning for different competitive Exams

Problem   1

----- Explanation   ----  

(11 × 7) - (5 × 3) = 77 - 15 = 62 

(18 × 3) - (5 × 4) = 54 - 20 = 34

(9 × 6) - (4 × 8) = 54 - 32 = 22    

 Problem  2

 ----- Explanation   ----  

2² + 5² + 3² + 7² = 4 + 25 + 9 + 49 = 87

8² + 5² + 4² + 3² = 64 + 25 + 16 + 9 = 114

9² + 4² + 1² + 6² = 81 + 16 + 1 + 36 = 134

  Problem   3

 ----- Explanation   ----  

 2 x (5 + 7 + 3) = 2 x 15 = 30 

8 x (5 + 4 + 3) = 8 x 12 = 96 

3 x (4 + 9 + 6) =  3 x 19 = 57  

 Problem   4

 ----- Explanation   ----  

 1² + (5 × 3 × 7) =1 + 105 = 106

4² + (5 × 3 × 6) =16 + 90 = 106

3² + (3 × 2 × 7) = 9 + 42 = 51 

 Problem 5

----- Explanation   ----  

   1² + (5 + 3 + 7) = 1 + 15 = 16

   4² + (5 + 3 + 6) = 16 + 14 = 30

   3² + (3 + 2 + 7)  = 9 + 12 = 21

 Problem 6

----- Explanation   ----  

(2 + 5)² + (7 - 3)² = 7² +4² =  49 + 16 = 65

(1 + 5)² + (6 - 3)² = 6² + 3² = 36 + 9 = 45 = ?

(2 + 3)² + (7 - 2)² = 5² + 5² = 25 + 25 = 50    

  Problem 7

----- Explanation   ----  

(1+2+3+4)² = 10² = 100

(2+3+4+5)² = 14² = 196

(4+5+6+7)² = 22² = 484 

 Problem 8

----- Explanation   ----  

LCM Of  1, 4, 3 and 2 = 12

LCM Of 3, 2, 5 and 4 = 60

LCM Of  4 , 5 ,6 and 2 = 60 = ? 

  Problem 9

----- Explanation   ----  

 19 + 16 + 15 + 12 = 62 ⇔26

23 + 22 + 27 + 19 = 91 ⇔19

24 + 23 + 20 + 22 = 89 ⇔98 

Problem 10

----- Explanation   ----  

√81+√16+√256+√25 = 9+4+16+5 = 34

√9+√49+√1+√64 = 3+7+1+8 = 19

√4+√36+√121+√289 = 2+6+11+7 = 26 = ?   

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