Speed-Time-Distance, Work-Time, Clocks & Calendars for GATE Aptitude 2027: Solved PYQs

Join the PiyushAI AI & Data Science Community | Newsletter

📬 PiyushAI · AI & Data Science Learning Community

Stay Ahead in AI, Data Science, Exams & Your Learning Journey

Join 20,000+ learners exploring AI & Data Science — GATE, Bank IT & PSU exam aspirants, IIT Madras BS Degree students, school teachers exploring the CBSE CT & AI curriculum, working professionals, and anyone starting their AI literacy journey. Tell us a little about yourself and get personalised updates, resources, and mentorship alerts — straight from Piyush Wairale.

🎯

Exam & Career Updates First

GATE, Bank IT Officer, PSU & Government job alerts — plus IIT Madras BS Degree guidance.

📚

Free Learning Resources

Study notes, PYQ analysis, practice questions & guides for exams, data science & AI.

🚀

AI Literacy & CBSE CT-AI

AI tools & concepts for everyone, CBSE CT & AI curriculum support for schools & teachers, plus early course access.

✍️ Join the Community — Fill the Form

Takes less than 60 seconds • No spam, only what helps you learn & grow

👨‍🎓 20,000+ Students

▶️ 44,000+ YouTube Subscribers

🎓 IIT Madras Alumnus Mentor

Quick Summary: Speed-Time-Distance, Work-Time, Clocks and Calendars give 2 to 4 marks in GATE General Aptitude 2027 across every paper (DA, RA, CS, ME, EE, CE, EC). They are all one idea in different clothes: rate × time = amount. Trains, boats, pipes, workers and clock hands are all rates. This guide covers the formulas, the relative-speed and LCM-work methods, the clock-angle formula, the odd-days calendar method, 8 solved previous-year and GATE-style questions, a 5-question practice set, a one-page formula sheet and the traps that cost a mark you had already earned.

🎯 Score 15/15 in General Aptitude. Practise this topic with 100+ exam-level questions, detailed solutions and All-India ranking in the Best GATE Aptitude Test Series 2027 by PiyushAI. Topic-wise tests + full-length GA mocks, valid till GATE 2027.

📋 Table of Contents

Why this topic matters in GATE GA
What the official GA syllabus says
Speed, time and distance: average speed and relative speed
Trains, boats and streams
Work and time, pipes and cisterns
Clocks
Calendars
Shortcuts and traps
Solved PYQs and GATE-style questions
Practice set
One-page formula sheet
Common mistakes
FAQs

Why this topic matters in GATE GA

This cluster is the oldest part of GATE General Aptitude. Trains crossing platforms, pipes filling tanks and workers finishing jobs have appeared since GA was introduced in 2010, and they still appear, now dressed as robots on a conveyor, servers processing requests or drones meeting mid-air. The arithmetic is the same: a rate multiplied by a time gives an amount, and when two rates act together they add (same direction) or subtract (opposite direction).

Clocks and calendars are smaller but they are pure marks for anybody who knows two formulas: the hand-angle formula and the odd-days rule. Across DA, RA, CS, ME, EE, CE and EC the GA section is common, so this chapter is worth the same 2 to 4 marks to every aspirant.

Here is roughly how much the cluster has contributed. Candidates targeting 15/15 in GA should solve any question here in 60 to 90 seconds.

Year	Marks from this topic (approximate, across papers)	Typical question type
2019	2 to 3	Two vehicles meeting, workers leaving midway
2020	1 to 3	Average speed, pipe with leak
2021	2 to 3	Train crossing a platform, clock angle
2022	2 to 4	Boat upstream and downstream, efficiency ratio
2023	2 to 3	Relative speed on a circular track, day of the week
2024	2 to 3	Work with alternating days, time-distance graph
2025	1 to 3	Escalator problem, hands overlapping
2026	2 to 3	Men-days-hours, calendar repetition

What the official GA syllabus says

Official GATE GA syllabus, Quantitative Aptitude: “Numerical computation and estimation: ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series. Mensuration and geometry. Elementary statistics and probability.”

Speed-time-distance, work-time, clocks and calendars are not named in the syllabus; they sit under “numerical computation and estimation” and under ratios (every one of them is an inverse-proportion problem). The complete GA syllabus and weightage are in the GATE General Aptitude 2027 hub. The previous post covered Data Interpretation.

Speed, time and distance: average speed and relative speed

Distance = Speed × Time. Units must match: 1 km/h = 5/18 m/s, so 72 km/h = 20 m/s and 36 km/h = 10 m/s. Memorise the factor 5/18 both ways.

Average speed = total distance / total time. For equal distances at speeds u and v, average = 2uv/(u + v). For equal times, average = (u + v)/2.
Relative speed: same direction, u − v; opposite direction, u + v. Time to meet = initial gap / relative speed.
Inverse proportion: for a fixed distance, speed × time is constant. If speed becomes 3/4 of the original, time becomes 4/3, so the delay is 1/3 of the usual time.
Meeting point from both ends: if two people start toward each other and meet after time t, the distances they cover are in the ratio of their speeds.
Circular track: same direction, they meet every L/(u − v); opposite direction, every L/(u + v), where L is the track length.

✅ Solved Example (GATE 2023 style): A car travels from P to Q at 40 km/h and returns at 60 km/h. What is the average speed for the round trip?
Solution: Equal distances, so average = 2 × 40 × 60/(40 + 60) = 4800/100 = 48 km/h. (Not 50. Check with distance 120 km: 3 h + 2 h = 5 h for 240 km, 48 km/h.)

✅ Solved Example (GATE 2023 style): Walking at 3/4 of his usual speed, a man reaches office 20 minutes late. What is his usual time?
Solution: Time becomes 4/3 of usual, so the extra time is 1/3 of usual = 20 min. Usual time = 60 minutes.

Trains, boats and streams

Trains: to cross a pole or a person, the train covers its own length. To cross a platform or bridge, it covers (train length + platform length). To cross another train, it covers the sum of both lengths at the relative speed.

Boats: if the boat’s speed in still water is b and the stream’s speed is s, then downstream speed = b + s and upstream speed = b − s. Reversed: b = (downstream + upstream)/2 and s = (downstream − upstream)/2.

Escalators work exactly like streams: a person walking on a moving escalator has speed (person + escalator) going with it and (person − escalator) going against.

✅ Solved Example (GATE 2023 style): A 180 m long train running at 54 km/h crosses a platform in 20 seconds. What is the length of the platform?
Solution: 54 km/h = 54 × 5/18 = 15 m/s. Distance covered in 20 s = 300 m = train + platform. Platform = 300 − 180 = 120 m.

✅ Solved Example (GATE 2023 style): A boat goes 24 km downstream in 2 hours and returns in 3 hours. Find the speed of the boat in still water and the speed of the stream.
Solution: Downstream = 12 km/h, upstream = 8 km/h. Boat = (12 + 8)/2 = 10 km/h, stream = (12 − 8)/2 = 2 km/h.

Work and time, pipes and cisterns

If A finishes a job in a days, A does 1/a of the job per day. Rates add: A and B together do 1/a + 1/b per day and finish in ab/(a + b) days. A pipe that empties is a negative rate.

The LCM method avoids fractions. Take the total work as the LCM of the individual times. If A takes 12 days and B takes 15 days, let the work be 60 units: A does 5 per day, B does 4 per day, together 9 per day, so 60/9 = 6.67 days.

Efficiency: if A is twice as efficient as B, A takes half the time. Efficiency ratio = inverse of the time ratio.
Men-days: M₁D₁H₁/W₁ = M₂D₂H₂/W₂. Men, days and hours multiply; work is the output.
Leaving midway: compute the work done before the person leaves, then the rate of those who remain.
Alternate days: compute the work done in one full cycle (A’s day plus B’s day), find how many full cycles fit, then finish the remainder day by day.
Wages are shared in the ratio of work done, which equals the ratio of rates if they worked equal time.

✅ Solved Example (GATE 2023 style): A can do a job in 10 days and B in 15 days. They start together, but A leaves after 4 days. In how many more days does B finish?
Solution: LCM = 30 units. A: 3/day, B: 2/day. In 4 days together: 4 × 5 = 20 units. Remaining 10 units at B’s 2/day = 5 days.

✅ Solved Example (GATE 2023 style): Pipe A fills a tank in 6 hours, pipe B fills it in 9 hours and pipe C empties it in 18 hours. If all three are opened together, how long does the tank take to fill?
Solution: LCM = 18 units. A: +3/h, B: +2/h, C: −1/h. Net = 4/h. Time = 18/4 = 4.5 hours.

Clocks

The minute hand moves 360° in 60 minutes: 6° per minute. The hour hand moves 360° in 12 hours: 0.5° per minute (30° per hour). The relative speed is 5.5° per minute.

Angle between the hands at H hours M minutes = |30H − 5.5M| (take 360 minus the result if it exceeds 180)

The hands overlap 11 times in 12 hours, every 65 5/11 minutes (720/11 minutes). First overlap after 12:00 is at 12:05:27.
They are at 180° 11 times in 12 hours and at 90° 22 times in 12 hours (44 times a day).
To find when the hands coincide after H o’clock: M = 60H/11 minutes past H. After 3 o’clock: 180/11 = 16 4/11 minutes.
A clock that gains or loses: if it gains x minutes per hour, in 24 hours it gains 24x minutes.

✅ Solved Example (GATE 2023 style): What is the angle between the hour and minute hands at 4:40?
Solution: |30 × 4 − 5.5 × 40| = |120 − 220| = 100°. (Check: minute hand at 240°, hour hand at 120 + 20 = 140°, difference 100°.)

✅ Solved Example (GATE 2023 style): At what time between 7 and 8 o’clock are the hands together?
Solution: M = 60 × 7/11 = 420/11 = 38 2/11 minutes. The hands coincide at 7:38 and 2/11 min, about 7:38:11.

Calendars

An ordinary year has 365 days = 52 weeks + 1 odd day. A leap year has 366 days = 52 weeks + 2 odd days. A year is leap if divisible by 4, except century years, which must be divisible by 400 (2000 was leap, 1900 and 2100 are not).

100 years contain 24 leap years and 76 ordinary years: 24 × 2 + 76 = 124 odd days = 17 weeks + 5 odd days.
200 years: 10 − 7 = 3 odd days. 300 years: 15 − 14 = 1 odd day. 400 years: 20 + 1 (for the year 400 itself) = 21 = 0 odd days. The calendar repeats every 400 years.
Odd days 0 to 6 map to Sunday to Saturday when counting from the start of the Gregorian calendar (1 January, year 1, was a Monday; day 0 of the count is Sunday).
Same weekday next year: a date advances by 1 weekday after an ordinary year and by 2 after a leap year (if 29 February lies in between).
Month odd days: January 3, February 0 (1 in a leap year), March 3, April 2, May 3, June 2, July 3, August 3, September 2, October 3, November 2, December 3.

✅ Solved Example (GATE 2023 style): If 15 August 2025 is a Friday, what day of the week is 15 August 2027?
Solution: From 15 Aug 2025 to 15 Aug 2026: 365 days, +1 odd day. From 15 Aug 2026 to 15 Aug 2027: 365 days (29 Feb 2028 is not in this range), +1 odd day. Total +2. Friday + 2 = Sunday.

✅ Solved Example (GATE 2023 style): What day of the week was 26 January 1950?
Solution: Up to 1949: 1600 years give 0 odd days; 300 years give 1; 49 years (1901 to 1949) have 12 leap years and 37 ordinary years: 24 + 37 = 61 = 5 odd days. Up to end of 1949: 6 odd days. Add 26 days of January 1950: 26 = 5 odd days. Total 11 = 4 odd days = Thursday.

Each of these sub-topics has a timed test with video solutions in the GATE Aptitude Test Series; the work-time test alone has 40 questions ranked against every other GATE 2027 aspirant.

Shortcuts and traps

💡 GATE Tip: Convert km/h to m/s with 5/18 the moment a train or platform length is given in metres. Mixed units cause more wrong answers than any formula.

💡 GATE Tip: For work problems, pick the total work as the LCM of the times. Every rate becomes an integer and the whole solution is addition.

💡 GATE Tip: When two objects start toward each other, the time to meet is gap/(u + v), and the meeting point splits the gap in the ratio u : v. You rarely need to solve an equation.

💡 GATE Tip: For a day-of-the-week question that spans a few years, just count +1 per ordinary year and +2 per leap year crossed. Only use the full odd-days method for dates centuries apart.

❌ Averaging the two speeds for a round trip. The answer is 2uv/(u + v), always less than (u + v)/2.
❌ Forgetting the train’s own length when it crosses a platform.
❌ Adding times instead of rates when two workers work together.
❌ Treating an emptying pipe as a positive rate.
❌ Using 30H − 6M for the clock angle; the hour hand moves too, so the coefficient of M is 5.5.
❌ Counting 1900 or 2100 as a leap year.
❌ Adding a leap-year +2 when 29 February is not actually between the two dates.

Solved previous-year and GATE-style questions

✅ Solved Example (GATE 2019): Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ____.
Solution: Relative speed = 60 − 50 = 10 km/h. Time = 20/10 = 2 hours.

✅ Solved Example (GATE 2013, CS): A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is: (A) 36 (B) 30 (C) 24 (D) 18
Solution: Take the total distance as 120 km. Train: 60 km at 60 km/h = 1 h. Bus: 30 km at 30 km/h = 1 h. Cycle: 30 km at 10 km/h = 3 h. Total 5 h for 120 km, average = 24 km/h. Answer: (C).

✅ Solved Example (GATE 2010, CS): 5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?
Solution: One skilled worker does 1/100 of the wall per day, one semi-skilled 1/200, one unskilled 1/300. Team rate = 2/100 + 6/200 + 5/300 = 6/300 + 9/300 + 5/300 = 20/300 = 1/15. The team takes 15 days.

✅ Solved Example (GATE 2011, CS): A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?
Solution: Let each truck ship c per day, daily orders be d and backlog be B. 28c = B + 4d and 30c = B + 10d. Subtracting, 2c = 6d, so d = c/3 and B = 28c − 4c/3 = 80c/3. In 5 days the orders to clear are B + 5d = 85c/3, so 5nc ≥ 85c/3 gives n ≥ 17/3 = 5.67. Minimum 6 trucks.

✅ Solved Example (GATE 2014): At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a clock make an angle closest to 60°? (A) 6:22 a.m. (B) 6:27 a.m. (C) 6:38 a.m. (D) 6:45 a.m.
Solution: Angle = |30 × 6 − 5.5M| = |180 − 5.5M| = 60 gives 5.5M = 120 or 240, so M = 21.8 or 43.6. The option closest to either is (A) 6:22 a.m. (at 6:22 the angle is 180 − 121 = 59°).

✅ Solved Example (GATE 2013): A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is: (A) 30 (B) 36 (C) 40 (D) 24
Solution: Total distance = 30 km in 45 minutes = 0.75 h. Average = 30/0.75 = 40 km/h. Answer: (C).

✅ Solved Example (GATE-style): Two trains of lengths 150 m and 250 m run at 60 km/h and 48 km/h in opposite directions. How long do they take to cross each other?
Solution: Relative speed = 108 km/h = 108 × 5/18 = 30 m/s. Distance = 150 + 250 = 400 m. Time = 400/30 = 13.33 seconds.

✅ Solved Example (GATE-style): 1 January 2024 was a Monday. What day of the week is 1 January 2028?
Solution: 2024 is a leap year (+2), 2025 (+1), 2026 (+1), 2027 (+1). Total +5. Monday + 5 = Saturday.

★ PiyushAI Test Series

Best GATE Aptitude Test Series 2027

General Aptitude is 15 marks in every GATE paper and the easiest 15 marks to lose to silly mistakes. The PiyushAI Aptitude Test Series by Piyush Wairale (IIT Madras) gives you topic-wise tests on exactly this chapter, full-length GA mocks in the real GATE interface, detailed video and text solutions, and All-India rank analysis.

✅ 30+ topic-wise tests

✅ Full-length GA mocks

✅ PYQs 2010 to 2026 solved

✅ All-India rank & analytics

✅ Works for every GATE paper

✅ Valid till GATE 2027

🚀 Join the GATE Aptitude Test Series →

Practice set

Attempt these in 7 minutes before opening the key.

A train 240 m long passes a pole in 12 seconds. Its speed in km/h is (A) 60 (B) 72 (C) 80 (D) 90
A and B together can do a job in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can A, B and C together finish it? (A) 8 (B) 10 (C) 12 (D) 6
A boat’s speed in still water is 9 km/h and the stream flows at 3 km/h. The time to go 24 km upstream and return is (A) 6 h (B) 5 h (C) 4 h (D) 8 h
The angle between the hands of a clock at 9:30 is (A) 90° (B) 105° (C) 120° (D) 75°
If 1 March 2025 is a Saturday, then 1 March 2026 is a (A) Saturday (B) Sunday (C) Monday (D) Friday

Show answer key

(B) 240/12 = 20 m/s = 20 × 18/5 = 72 km/h.
(B) LCM 60: A+B = 5, B+C = 4, C+A = 3 units/day. Sum = 12 = 2(A+B+C), so A+B+C = 6/day; 60/6 = 10 days.
(A) Upstream 6 km/h: 4 h. Downstream 12 km/h: 2 h. Total 6 h.
(B) |30 × 9 − 5.5 × 30| = |270 − 165| = 105°.
(B) 1 Mar 2025 to 1 Mar 2026 spans 365 days (no 29 Feb in between): +1. Sunday.

One-page formula sheet

1. Distance = speed × time. 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h.
2. Average speed = total distance / total time. Equal distances: 2uv/(u + v). Equal times: (u + v)/2.
3. Relative speed: same direction u − v, opposite u + v. Time to meet = gap / relative speed.
4. Fixed distance: speed and time are inversely proportional. Speed × a/b gives time × b/a.
5. Train crossing pole: own length. Crossing platform: own length + platform. Crossing train: sum of lengths at relative speed.
6. Boat: downstream b + s, upstream b − s; b = (D + U)/2, s = (D − U)/2.
7. Work: rate = 1/time; rates add; together ab/(a + b). Emptying pipe is negative. Use LCM as total work.
8. M₁D₁H₁/W₁ = M₂D₂H₂/W₂. Efficiency ratio = inverse of time ratio.
9. Clock angle = |30H − 5.5M|; if over 180, subtract from 360. Hands coincide at M = 60H/11 past H.
10. Hands overlap 11 times, are opposite 11 times and perpendicular 22 times in 12 hours.
11. Odd days: ordinary year 1, leap year 2, 100 years 5, 200 years 3, 300 years 1, 400 years 0.
12. Leap year: divisible by 4, but century years only if divisible by 400. Same date next year moves +1 (or +2 across 29 Feb).

Common mistakes

❌ Answering “time to be 20 km apart” with the time to meet, or the reverse. Read whether the vehicles move toward or away from each other.
❌ Using the relative speed u − v when the objects move in opposite directions.
❌ Finishing a work problem at the fractional day (6.67) when the question asks for whole days needed (7).
❌ Taking the clock angle greater than 180° as the answer when the reflex angle was not asked.
❌ Counting the leap-year day when the date range does not include 29 February.
❌ Forgetting that “the end of the 4th day” means 4 full days of shipping, not 3.

FAQs

How many questions from this cluster appear in GATE GA?

Usually 1 to 2 questions worth 2 to 4 marks per paper. Speed-time-distance and work-time are the most frequent; clocks and calendars appear once every two or three years.

Which is the single most useful formula here?

Average speed over equal distances = 2uv/(u + v). It appears in GATE more often than any other formula in this chapter, and the trap option (u + v)/2 is always present.

Should I learn the odd-days method or just count year by year?

For GATE, year-by-year counting (+1 ordinary, +2 leap) handles almost every question. Learn the century odd days (5, 3, 1, 0) only as a backup for a date centuries away.

Is the PiyushAI Aptitude Test Series enough for GA?

Yes. The Best GATE Aptitude Test Series 2027 has topic tests on speed-time-distance, work-time and clocks-calendars, tests on every other GA chapter, full-length GA mocks in the GATE interface, solved PYQs from 2010 to 2026 and All-India rank analysis. Together with the free guides on this site, it covers the whole GA section.

Do I need to memorise the clock overlap times?

No. Derive them from M = 60H/11 when needed. The only facts worth memorising are the relative speed of 5.5° per minute and the 11 overlaps per 12 hours.

Stop losing easy marks. Practise this topic under exam pressure.

Enroll in the Best GATE Aptitude Test Series →

Previous in series: Data Interpretation for GATE Aptitude 2027 | Next in series: Logical Deduction & Induction for GATE Aptitude 2027