Races and Circular Motion Questions with Solutions | Set 4 (Q31 to Q35)

This set contains Races and Circular Motion Questions with Solutions — Set 4 (Q31 to Q35) covering a mix of question types and difficulty levels — from basic to advanced — exactly as asked in real competitive exams.

Solutions are written in a simple, step-by-step notebook style for easy self-study and quick understanding. Each solution is broken down step by step so even the toughest question feels easy. These questions are hand-picked for students preparing for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and all campus placement aptitude tests. International students preparing for GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests will find these equally useful.

✏️ Attempt each question on your own first — then check the solution below.

31. In a 1 km race, the speeds of A and B are in the ratio of 5 : 3 and A wins by 10 seconds. Find the time taken by B to finish the race and distance covered by B when A finishes the race.

32. A and B are running on a circular track in opposite direction from same time at same point with speed of 81 m/sec and 6 m/sec respectively. If the length of the circular track be 960 m, how many times distinct points they will meet.

33. A and B run a 12 km race on a circular track of length 1200 m. They complete one round in 300 sec and 400 sec respectively. After how much time from start will the faster person meet the slower person for the last time.

34. A and B run around a circular track of length 1100 m in opposite direction with initial speed of 6 m/sec and 4 m/sec respectively. Starting from the same point whenever they meet, A’s speed halves and B’s speed doubles. After how much time from the beginning will they meet for the second time ?

35. Three persons A, B and C run along a circular track at speed of 3 km/h, 4 km/h and 6 km/h respectively. If the length of the track is 36 km, then after how much time will they meet again at the starting point.

31. In a 1 km race, the speeds of A and B are in the ratio of 5 : 3 and A wins by 10 seconds. Find the time taken by B to finish the race and distance covered by B when A finishes the race.
Sol:
Distance is constant
∴ Time ∝ \(\frac{1}{{Speed}}\)

⟹ \(\frac{3}{5} = \frac{t}{{t + 10}}\)
t = 15 sec
∴ time taken by B to finish the race = 15 + 10= 25 sec       Answer
B takes 25 sec to cover 1000 m
∴ in 15 se B will cover = \(\frac{{15}}{{25}} \times 1000\) = 600 m     Answer

32. A and B are running on a circular track in opposite direction from same time at same point with speed of 81 m/sec and 6 m/sec respectively. If the length of the circular track be 960 m, how many times distinct points they will meet.
Sol:
4 : 3 ⟹ 4 + 3 = 7 times      Answer

33. A and B run a 12 km race on a circular track of length 1200 m. They complete one round in 300 sec and 400 sec respectively. After how much time from start will the faster person meet the slower person for the last time.
Sol:
Number of rounds = \(\frac{{12 \times 1000}}{{1200}}\) = 10 rounds
Speed of A = \(\frac{{1200}}{{300}}\) = 4 m/sec
Speed of B = \(\frac{{1200}}{{400}}\) = 3 m/sec

So in 1200 sec A will complete \(\frac{{1200}}{{300}}\) = 4 rounds
& in 1200 sec B will complete \(\frac{{1200}}{{400}}\) = 3 rounds
So after A’s 4 rounds they will meet first time after A’s next 4 round they will meet second time 7 number of rounds are 10 (maximum by A)
So they will meet last time after 8 rounds of A & time taken by A to complete one round = 300 se
So they will meet last time after = 8 × 300 sec
= 2400 sec     Answer

34. A and B run around a circular track of length 1100 m in opposite direction with initial speed of 6 m/sec and 4 m/sec respectively. Starting from the same point whenever they meet, A’s speed halves and B’s speed doubles. After how much time from the beginning will they meet for the second time ?
Sol:
1ˢᵗ meeting = \(\frac{{1100}}{{4 + 6}}\) = 110 m
2ⁿᵈ meeting = \(\frac{{1100}}{{\frac{6}{2} + 4 \times 2}}\) = 100 sec
∴ From starting time for 2ⁿᵈ meeting = 110 + 100 = 210m    Answer

35. Three persons A, B and C run along a circular track at speed of 3 km/h, 4 km/h and 6 km/h respectively. If the length of the track is 36 km, then after how much time will they meet again at the starting point.
Sol:
Time taken by A = \(\frac{{36}}{3}\) = 12 h
Time taken by A = \(\frac{{36}}{4}\) = 9 h
Time taken by A = \(\frac{{36}}{6}\) = 6 h
They will meet at the starting point after = LCM(12, 9, 6) = 36 h      Answer

✅ Well done on completing Set 4!

You can revisit the Races and Circular Motion Concept Page to strengthen your formulas and tricks before moving ahead.

Consistent practice is the key to mastering races and circular motion for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and international exams including GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests. Want to understand the concept better? Read about Circular Motion on Wikipedia before attempting the next set.

This page is part of our complete series of races and circular motion questions with solutions for competitive exams — covering every question type from basic to advanced so you can build speed, accuracy and confidence. Practising these questions regularly will also strengthen your core races and circular motion concept before your exam day.