Questions
1–2 questions per paper
Difficulty
Medium
Importance
High yield for quick marks
Overview
This topic covers essential arithmetic and logical reasoning concepts frequently tested in PSU recruitment exams. Mastering these areas allows students to secure quick marks by applying standardized formulas to patterns in time, speed, and dates. Understanding the underlying relationships between rates and cycles is the key to solving these problems efficiently.
Clocks & Calendars
Clock problems focus on the angle between hands and occurrences like coincidences, while calendar problems rely on the calculation of odd days. Success here depends on tracking the movement speed of the minute and hour hands and the cyclic nature of weeks.
- Angle between hands formula: |30H - 5.5M|
- Minute hand gains 5.5 degrees per minute relative to the hour hand
- Leap year logic: 366 days (divisible by 4, not 100 unless 400)
- Odd days: Number of days beyond complete weeks
- 100 years contain 5 odd days
Boats, Streams, Pipes & Cisterns
These are essentially variations of time, speed, and distance problems. In streams, you must account for relative speed based on current direction, while pipes and cisterns treat filling or emptying as rate-based work.
- Downstream speed: u + v (where u=boat, v=stream)
- Upstream speed: u - v
- Pipes and cisterns: Work done = (Rate of inlet - Rate of outlet)
- If a pipe fills in 'a' hours, rate is 1/a of the tank per hour
- Combined work formula: (xy)/(x+y) for two pipes filling
Train Problems
Train problems require careful handling of length units and relative velocity. You must correctly determine whether the total distance involves the length of the train alone or includes the length of a platform or another train.
- Relative speed: Added if moving in opposite directions, subtracted if same
- Distance covered = Length of train + Length of stationary object
- Conversion factor: multiply km/hr by 5/18 to get m/s
- Time = Total Distance / Relative Speed
- Passing a pole: Distance = length of train
Formula Sheet
Angle = |30H - 5.5M|
Downstream = u + v
Upstream = u - v
Speed in m/s = Speed in km/hr * (5/18)
Exam Tip
Always convert all units to a single system (e.g., m/s or hours) before performing any calculation to avoid common sign and magnitude errors.
Common Mistakes
- Forgetting to subtract or add the stream speed correctly when calculating relative velocity in boat problems.
- Ignoring the length of the platform or bridge when calculating total distance in train problems.
- Miscalculating 'odd days' by failing to account for non-leap century years correctly.
More Revision Notes
Ready to test yourself?
Play topic-wise Clocks, Calendars & Miscellaneous questions in Aspirant Arcade — gamified MCQ practice.
Download Free