Imagine a bus that covers 180 km in 6 hours. How fast does it go? Time and Distance problems all rest on one small relation between three things: speed, distance and time .
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Q1. Car A travels at 56 km/hr and reaches its destination in 4 hours. Car B travels at 52 km/hr and reaches its destination in 8 hours. What is the ratio of the distance covered by car A to that covered by car B?
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Answer: C
Distance = speed x time, for each car. Distance covered by A = 56 x 4 = 224 km. Distance covered by B = 52 x 8 = 416 km. Ratio of distances = 224 : 416. Divide both terms by their HCF, 32: 224/32 : 416/32 = 7 : 13. Check: 7 x 32 = 224 and 13 x 32 = 416, so the simplified ratio is correct.
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Q2. Car A travels at 70 km/hr and reaches its destination in 5 hours. Car B travels at 80 km/hr and reaches its destination in 4 hours. What is the ratio of the distance covered by car A to that covered by car B?
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Answer: D
Distance = speed x time, for each car. Distance covered by A = 70 x 5 = 350 km. Distance covered by B = 80 x 4 = 320 km. Ratio of distances = 350 : 320. Divide both terms by their HCF, 10: 350/10 : 320/10 = 35 : 32. Check: 35 x 10 = 350 and 32 x 10 = 320, so the simplified ratio is correct.
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Q3. Car A travels at 54 km/hr and reaches its destination in 7 hours. Car B travels at 60 km/hr and reaches its destination in 8 hours. What is the ratio of the distance covered by car A to that covered by car B?
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Answer: B
Distance = speed x time, for each car. Distance covered by A = 54 x 7 = 378 km. Distance covered by B = 60 x 8 = 480 km. Ratio of distances = 378 : 480. Divide both terms by their HCF, 6: 378/6 : 480/6 = 63 : 80. Check: 63 x 6 = 378 and 80 x 6 = 480, so the simplified ratio is correct.
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Q4. Car A travels at 56 km/hr and reaches its destination in 8 hours. Car B travels at 86 km/hr and reaches its destination in 2 hours. What is the ratio of the distance covered by car A to that covered by car B?
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Answer: C
Distance = speed x time, for each car. Distance covered by A = 56 x 8 = 448 km. Distance covered by B = 86 x 2 = 172 km. Ratio of distances = 448 : 172. Divide both terms by their HCF, 4: 448/4 : 172/4 = 112 : 43. Check: 112 x 4 = 448 and 43 x 4 = 172, so the simplified ratio is correct.
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Q5. Manish and Rohit start walking towards each other at the same time from two towns 36 km apart, at 10 km/hr and 8 km/hr respectively. After how many hours will they meet?
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Answer: D
Let Manish’s speed = 10 km/hr and Rohit’s speed = 8 km/hr. They move towards each other, so relative speed = 10 + 8 = 18 km/hr. Distance apart = 36 km. Time to meet = distance / relative speed. Time = 36 / 18 = 2 hours. Check: Manish covers 10 x 2 = 20 km. Rohit covers 8 x 2 = 16 km. 20 + 16 = 36 km, matching the total distance.
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Q6. Kavya and Manish start walking towards each other at the same time from two towns 36 km apart, at 11 km/hr and 7 km/hr respectively. After how many hours will they meet?
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Answer: A
Let Kavya’s speed = 11 km/hr and Manish’s speed = 7 km/hr. They move towards each other, so relative speed = 11 + 7 = 18 km/hr. Distance apart = 36 km. Time to meet = distance / relative speed. Time = 36 / 18 = 2 hours. Check: Kavya covers 11 x 2 = 22 km. Manish covers 7 x 2 = 14 km. 22 + 14 = 36 km, matching the total distance.
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Q7. Rohit and Kavya start walking towards each other at the same time from two towns 27 km apart, at 4 km/hr and 5 km/hr respectively. After how many hours will they meet?
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Answer: B
Let Rohit’s speed = 4 km/hr and Kavya’s speed = 5 km/hr. They move towards each other, so relative speed = 4 + 5 = 9 km/hr. Distance apart = 27 km. Time to meet = distance / relative speed. Time = 27 / 9 = 3 hours. Check: Rohit covers 4 x 3 = 12 km. Kavya covers 5 x 3 = 15 km. 12 + 15 = 27 km, matching the total distance.
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Q8. Isha and Rohit start walking towards each other at the same time from two towns 11 km apart, at 4 km/hr and 7 km/hr respectively. After how many hours will they meet?
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Answer: C
Let Isha’s speed = 4 km/hr and Rohit’s speed = 7 km/hr. They move towards each other, so relative speed = 4 + 7 = 11 km/hr. Distance apart = 11 km. Time to meet = distance / relative speed. Time = 11 / 11 = 1 hours. Check: Isha covers 4 x 1 = 4 km. Rohit covers 7 x 1 = 7 km. 4 + 7 = 11 km, matching the total distance.
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Q9. Isha and Manish start walking towards each other at the same time from two towns 36 km apart, at 10 km/hr and 8 km/hr respectively. After how many hours will they meet?
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Answer: D
Let Isha’s speed = 10 km/hr and Manish’s speed = 8 km/hr. They move towards each other, so relative speed = 10 + 8 = 18 km/hr. Distance apart = 36 km. Time to meet = distance / relative speed. Time = 36 / 18 = 2 hours. Check: Isha covers 10 x 2 = 20 km. Manish covers 8 x 2 = 16 km. 20 + 16 = 36 km, matching the total distance.
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Q10. Rohit and Kavya start walking towards each other at the same time from two towns 85 km apart, at 6 km/hr and 11 km/hr respectively. After how many hours will they meet?
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Answer: B
Let Rohit’s speed = 6 km/hr and Kavya’s speed = 11 km/hr. They move towards each other, so relative speed = 6 + 11 = 17 km/hr. Distance apart = 85 km. Time to meet = distance / relative speed. Time = 85 / 17 = 5 hours. Check: Rohit covers 6 x 5 = 30 km. Kavya covers 11 x 5 = 55 km. 30 + 55 = 85 km, matching the total distance.
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Q11. Isha and Rohit start walking towards each other at the same time from two towns 16 km apart, at 7 km/hr and 9 km/hr respectively. After how many hours will they meet?
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Answer: A
Let Isha’s speed = 7 km/hr and Rohit’s speed = 9 km/hr. They move towards each other, so relative speed = 7 + 9 = 16 km/hr. Distance apart = 16 km. Time to meet = distance / relative speed. Time = 16 / 16 = 1 hours. Check: Isha covers 7 x 1 = 7 km. Rohit covers 9 x 1 = 9 km. 7 + 9 = 16 km, matching the total distance.
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Q12. Isha and Rohit start walking towards each other at the same time from two towns 18 km apart, at 5 km/hr and 4 km/hr respectively. After how many hours will they meet?
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Answer: C
Let Isha’s speed = 5 km/hr and Rohit’s speed = 4 km/hr. They move towards each other, so relative speed = 5 + 4 = 9 km/hr. Distance apart = 18 km. Time to meet = distance / relative speed. Time = 18 / 9 = 2 hours. Check: Isha covers 5 x 2 = 10 km. Rohit covers 4 x 2 = 8 km. 10 + 8 = 18 km, matching the total distance.
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Q13. Manish and Isha start walking towards each other at the same time from two towns 55 km apart, at 5 km/hr and 6 km/hr respectively. After how many hours will they meet?
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Answer: A
Let Manish’s speed = 5 km/hr and Isha’s speed = 6 km/hr. They move towards each other, so relative speed = 5 + 6 = 11 km/hr. Distance apart = 55 km. Time to meet = distance / relative speed. Time = 55 / 11 = 5 hours. Check: Manish covers 5 x 5 = 25 km. Isha covers 6 x 5 = 30 km. 25 + 30 = 55 km, matching the total distance.
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Q14. Rohit and Kavya start walking towards each other at the same time from two towns 75 km apart, at 6 km/hr and 9 km/hr respectively. After how many hours will they meet?
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Answer: B
Let Rohit’s speed = 6 km/hr and Kavya’s speed = 9 km/hr. They move towards each other, so relative speed = 6 + 9 = 15 km/hr. Distance apart = 75 km. Time to meet = distance / relative speed. Time = 75 / 15 = 5 hours. Check: Rohit covers 6 x 5 = 30 km. Kavya covers 9 x 5 = 45 km. 30 + 45 = 75 km, matching the total distance.
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Q15. Manish and Isha start walking towards each other at the same time from two towns 85 km apart, at 10 km/hr and 7 km/hr respectively. After how many hours will they meet?
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Answer: D
Let Manish’s speed = 10 km/hr and Isha’s speed = 7 km/hr. They move towards each other, so relative speed = 10 + 7 = 17 km/hr. Distance apart = 85 km. Time to meet = distance / relative speed. Time = 85 / 17 = 5 hours. Check: Manish covers 10 x 5 = 50 km. Isha covers 7 x 5 = 35 km. 50 + 35 = 85 km, matching the total distance.
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Q16. Rohit and Isha start walking towards each other at the same time from two towns 28 km apart, at 7 km/hr and 7 km/hr respectively. After how many hours will they meet?
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Answer: D
Let Rohit’s speed = 7 km/hr and Isha’s speed = 7 km/hr. They move towards each other, so relative speed = 7 + 7 = 14 km/hr. Distance apart = 28 km. Time to meet = distance / relative speed. Time = 28 / 14 = 2 hours. Check: Rohit covers 7 x 2 = 14 km. Isha covers 7 x 2 = 14 km. 14 + 14 = 28 km, matching the total distance.
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Q17. Kritika starts cycling from a point at 10 km/hr. 2 hours later, Aditya sets out from the same point along the same road at 12 km/hr, chasing Kritika. After how many hours from Aditya’s start will Aditya catch up with Kritika?
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Answer: C
Let Kritika’s speed = 10 km/hr and Aditya’s speed = 12 km/hr. Kritika gets a head start of 2 hours. Head-start distance = 10 x 2 = 20 km. Both move in the same direction, so relative speed = 12 – 10 = 2 km/hr. Time to catch up = head-start distance / relative speed. Time = 20 / 2 = 10 hours. Check: in 10 hours, Aditya covers 12 x 10 = 120 km. Kritika covers 20 + 10 x 10 = 120 km, matching.
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Q18. Vikram starts cycling from a point at 10 km/hr. 1.5 hours later, Simran sets out from the same point along the same road at 15 km/hr, chasing Vikram. After how many hours from Simran’s start will Simran catch up with Vikram?
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Answer: A
Let Vikram’s speed = 10 km/hr and Simran’s speed = 15 km/hr. Vikram gets a head start of 1.5 hours. Head-start distance = 10 x 1.5 = 15 km. Both move in the same direction, so relative speed = 15 – 10 = 5 km/hr. Time to catch up = head-start distance / relative speed. Time = 15 / 5 = 3 hours. Check: in 3 hours, Simran covers 15 x 3 = 45 km. Vikram covers 15 + 10 x 3 = 45 km, matching.
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Q19. Aditya starts cycling from a point at 8 km/hr. 1 hour later, Kritika sets out from the same point along the same road at 16 km/hr, chasing Aditya. After how many hours from Kritika’s start will Kritika catch up with Aditya?
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Answer: B
Let Aditya’s speed = 8 km/hr and Kritika’s speed = 16 km/hr. Aditya gets a head start of 1 hours. Head-start distance = 8 x 1 = 8 km. Both move in the same direction, so relative speed = 16 – 8 = 8 km/hr. Time to catch up = head-start distance / relative speed. Time = 8 / 8 = 1 hours. Check: in 1 hours, Kritika covers 16 x 1 = 16 km. Aditya covers 8 + 8 x 1 = 16 km, matching.
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Q20. Aditya starts cycling from a point at 8 km/hr. 1.5 hours later, Simran sets out from the same point along the same road at 12 km/hr, chasing Aditya. After how many hours from Simran’s start will Simran catch up with Aditya?
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Answer: C
Let Aditya’s speed = 8 km/hr and Simran’s speed = 12 km/hr. Aditya gets a head start of 1.5 hours. Head-start distance = 8 x 1.5 = 12 km. Both move in the same direction, so relative speed = 12 – 8 = 4 km/hr. Time to catch up = head-start distance / relative speed. Time = 12 / 4 = 3 hours. Check: in 3 hours, Simran covers 12 x 3 = 36 km. Aditya covers 12 + 8 x 3 = 36 km, matching.
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Q21. Aditya starts cycling from a point at 6 km/hr. 1 hour later, Vikram sets out from the same point along the same road at 8 km/hr, chasing Aditya. After how many hours from Vikram’s start will Vikram catch up with Aditya?
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Answer: B
Let Aditya’s speed = 6 km/hr and Vikram’s speed = 8 km/hr. Aditya gets a head start of 1 hours. Head-start distance = 6 x 1 = 6 km. Both move in the same direction, so relative speed = 8 – 6 = 2 km/hr. Time to catch up = head-start distance / relative speed. Time = 6 / 2 = 3 hours. Check: in 3 hours, Vikram covers 8 x 3 = 24 km. Aditya covers 6 + 6 x 3 = 24 km, matching.
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Q22. Simran starts cycling from a point at 4 km/hr. 2 hours later, Vikram sets out from the same point along the same road at 12 km/hr, chasing Simran. After how many hours from Vikram’s start will Vikram catch up with Simran?
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Answer: A
Let Simran’s speed = 4 km/hr and Vikram’s speed = 12 km/hr. Simran gets a head start of 2 hours. Head-start distance = 4 x 2 = 8 km. Both move in the same direction, so relative speed = 12 – 4 = 8 km/hr. Time to catch up = head-start distance / relative speed. Time = 8 / 8 = 1 hours. Check: in 1 hours, Vikram covers 12 x 1 = 12 km. Simran covers 8 + 4 x 1 = 12 km, matching.
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Q23. Aditya starts cycling from a point at 10 km/hr. 1 hour later, Kritika sets out from the same point along the same road at 12 km/hr, chasing Aditya. After how many hours from Kritika’s start will Kritika catch up with Aditya?
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Answer: D
Let Aditya’s speed = 10 km/hr and Kritika’s speed = 12 km/hr. Aditya gets a head start of 1 hours. Head-start distance = 10 x 1 = 10 km. Both move in the same direction, so relative speed = 12 – 10 = 2 km/hr. Time to catch up = head-start distance / relative speed. Time = 10 / 2 = 5 hours. Check: in 5 hours, Kritika covers 12 x 5 = 60 km. Aditya covers 10 + 10 x 5 = 60 km, matching.
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Q24. Kritika starts cycling from a point at 8 km/hr. 1.5 hours later, Vikram sets out from the same point along the same road at 11 km/hr, chasing Kritika. After how many hours from Vikram’s start will Vikram catch up with Kritika?
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Answer: A
Let Kritika’s speed = 8 km/hr and Vikram’s speed = 11 km/hr. Kritika gets a head start of 1.5 hours. Head-start distance = 8 x 1.5 = 12 km. Both move in the same direction, so relative speed = 11 – 8 = 3 km/hr. Time to catch up = head-start distance / relative speed. Time = 12 / 3 = 4 hours. Check: in 4 hours, Vikram covers 11 x 4 = 44 km. Kritika covers 12 + 8 x 4 = 44 km, matching.
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Q25. Kritika starts cycling from a point at 8 km/hr. 1 hour later, Simran sets out from the same point along the same road at 12 km/hr, chasing Kritika. After how many hours from Simran’s start will Simran catch up with Kritika?
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Answer: C
Let Kritika’s speed = 8 km/hr and Simran’s speed = 12 km/hr. Kritika gets a head start of 1 hours. Head-start distance = 8 x 1 = 8 km. Both move in the same direction, so relative speed = 12 – 8 = 4 km/hr. Time to catch up = head-start distance / relative speed. Time = 8 / 4 = 2 hours. Check: in 2 hours, Simran covers 12 x 2 = 24 km. Kritika covers 8 + 8 x 2 = 24 km, matching.
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