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- Question
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Options- A. 5 kmph
- B. 6 kmph
- C. 6.25 kmph
- D. 7.5 kmph
- Correct Answer
- 5 kmph
ExplanationLet Abhay's speed be x km/hr.Then, 30 - 30 = 3 x 2x ⟹ 6x = 30
⟹ x = 5 km/hr.
Time and Distance problems
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- 1. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options- A. 9
- B. 10
- C. 12
- D. 20 Discuss
Correct Answer: 10
Explanation:
Due to stoppages, it covers 9 km less.Time taken to cover 9 km = ❨ 9 x 60 ❩min = 10 min. 54 - 2. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Options- A. 35.55 km/hr
- B. 36 km/hr
- C. 71.11 km/hr
- D. 71 km/hr Discuss
Correct Answer: 71.11 km/hr
Explanation:
Total time taken = ❨ 160 + 160 ❩hrs. = 9 hrs. 64 80 2 ∴ Average speed = ❨ 320 x 2 ❩km/hr = 71.11 km/hr. 9 - 3. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Options- A. 3.6
- B. 7.2
- C. 8.4
- D. 10 Discuss
Correct Answer: 7.2
Explanation:
Speed = ❨ 600 ❩m/sec. 5 x 60 = 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= ❨ 2 x 18 ❩ km/hr 5 = 7.2 km/hr.
- 4. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:
Options- A. 14 km
- B. 15 km
- C. 16 km
- D. 17 km Discuss
Correct Answer: 16 km
Explanation:
Let the distance travelled on foot be x km.Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9 4 9 ⟹ 9x + 4(61 -x) = 9 x 36
⟹ 5x = 80
⟹ x = 16 km.
- 5. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1⅔ hours, it must travel at a speed of:
Options- A. 300 kmph
- B. 360 kmph
- C. 600 kmph
- D. 720 kmph Discuss
Correct Answer: 720 kmph
Explanation:
Distance = (240 x 5) = 1200 km.Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1⅔ hours as 5/3 hours]
∴ Required speed = ❨ 1200 x 3 ❩km/hr = 720 km/hr. 5 - 6. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
Options- A. 2 : 3
- B. 3 : 2
- C. 3 : 4
- D. 4 : 3 Discuss
Correct Answer: 3 : 4
Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr.Then, 120 + 480 = 8 ⟹ 1 + 4 = 1 ....(i) x y x y 15 And, 200 + 400 = 25 ⟹ 1 + 2 = 1 ....(ii) x y 3 x y 24 Solving (i) and (ii), we get: x = 60 and y = 80.
∴ Ratio of speeds = 60 : 80 = 3 : 4.
- 7. A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:
Options- A. 35
- B.
36 2 3 - C.
37 1 2 - D. 40 Discuss
Correct Answer: 40
Explanation:
Let distance = x km and usual rate = y kmph.Then, x - x = 40 ⟹ 2y(y + 3) = 9x ....(i) y y + 3 60 And, x - x = 40 ⟹ y(y - 2) = 3x ....(ii) y -2 y 60 On dividing (i) by (ii), we get: x = 40.
- 8. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Options- A. 8 kmph
- B. 11 kmph
- C. 12 kmph
- D. 14 kmph Discuss
Correct Answer: 12 kmph
Explanation:
Let the distance travelled by x km.Then, x - x = 2 10 15 ⟹ 3x - 2x = 60
⟹ x = 60 km.
Time taken to travel 60 km at 10 km/hr = ❨ 60 ❩hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
∴ Required speed = ❨ 60 ❩kmph. = 12 kmph. 5 - 9. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
Options- A.
13 1 days 3 - B. 15 days
- C. 20 days
- D. 26 days Discuss
Correct Answer:13 1 days 3
Explanation:
Work done by X in 8 days = ❨ 1 x 8 ❩ = 1 . 40 5 Remaining work = ❨ 1 - 1 ❩ = 4 . 5 5 Now, 4 work is done by Y in 16 days. 5 Whole work will be done by Y in ❨ 16 x 5 ❩ = 20 days. 4 ∴ X's 1 day's work = 1 , Y's 1 day's work = 1 . 40 20 (X + Y)'s 1 day's work = ❨ 1 + 1 ❩ = 3 . 40 20 40 Hence, X and Y will together complete the work in ❨ 40 ❩ = 13 1 days. 3 3 - 10. A and B can do a job together in 7 days. A is 1¾ times as efficient as B. The same job can be done by A alone in :
Options- A.
9 1 days 3 - B. 11 days
- C.
12 1 days 4 - D.
16 1 days 3
Discuss
Correct Answer: 11 days
Explanation:
(A's 1 day's work) : (B's 1 day's work) = 7 : 1 = 7 : 4. 4 Let A's and B's 1 day's work be 7x and 4x respectively.
Then, 7x + 4x = 1 ⟹ 11x = 1 ⟹ x = 1 . 7 7 77 ∴ A's 1 day's work = ❨ 1 x 7 ❩ = 1 . 77 11
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