Time and Distance - Aptitude Questions and Answers Part 2

6. On his way to office, Rohan's taxi driver drives him at a speed of 30 kmph and reaches late by one-third of an hour. Next morning, he drives at a speed of 45 kmph but is still 8 minutes late. Find the distance between his home and office?

a. 18 km
b. 20 km
c. 27 km
d. 35 km

Answer: a. 18 km

Explanation:

D = S x T
∴ S =D; T =D
TS


Let distance be D
With speed 30km/hr he is 20 minutes (one-third of an hour) late
With speed 45 km/hr he is 8 minutes late
∴ Difference between two times = 20-8 = 12 min =12hours
60

Tip:
Difference between two given times can also be easily measured or checked by looking at a watch or imagining a watch.


Also, time = T =D
S
∴D-D=12
304560
∴ D = 18 km


7. A child goes to school on bike at a speed of 18 km/h.  While coming back, he take school bus which runs faster by 27 km/h. What is his average speed for the entire journey?

a. 25.71 km/hr
b. 27 km/hr
c. 27.39 km/hr
d. 31.5km/hr

Answer: a. 25.71 km/hr

Explanation:

D = S x T
∴ S =D; T =D
TS


Speed = S =D
T
Average Speed =Total distance travelled
Total time taken
Let distance between start and end be D
Total distance travelled = D+D = 2D
The bus runs 27 kmph faster, so its speed is 45 kmph.
Total Time = t1+t2 =d1+d2=D+D
s1s21845
∴ Average speed =2D= 25.71 km/hr
D/18 + D/45


8. A friend of mine covers a total distance of 325 km from his hotel to village by three different modes.  He travels first 96 km in a rickshaw, 124 km by bus and 105 km by bullock cart. The speed of rickshaw is 16 km/hr, bus is 31 km/h and bullock cart is 7 km/h. What is his average speed for the entire travel?

a. 13 km/hr
b. 14.25 km/hr
c. 18 km/hr
d. 16.75 km/hr

Answer: a. 13 km/hr

Explanation:

D = S x T
∴ S =D; T =D
TS


Speed = S =D
T
Average Speed =Total distance travelled
Total time taken
Total distance = 96 + 124 + 105 = 325 km
Total Time = t1+t2+t3 =d1+d2+d3=96+124+105= 25 hours
s1s2s316317
∴ Average speed =325= 13 km/hr
25


9. Rajat travels from City A to City B. He travels first 25% of the distance at 20 kmph, next 25% of the distance at half the earlier speed and the remaining distance at 80 kmph. Find his average speed for the travel.

a. 22.85 km/hr
b. 25.15 km/hr
c. 40 km/hr
d. 50 km/hr

Answer: a. 22.85 km/hr

Explanation:

D = S x T
∴ S =D; T =D
TS


Speed = S =D
T
Average Speed =Total distance travelled
Total time taken
Let Total distance = D km
Parts of the distance =D;D; remaining distance.
44
Remaining distance = D - (D+D) =D
442
Half the earlier speed in second segment of travel = 10 kmph
Total Time = t1+t2+t3 =D+D+D=D+D+D=7D
4 x 204 x 102 x 808040160160
∴ Average speed =D= 22.85 km/hr
7D/160


10. To meet a friend in 6 minutes, Reeta drives at 40 kmph. If she could take 2 minutes more to meet her friend, at what speed could she drive?

a. 15 km/hr
b. 18 km/hr
c. 21 km/hr
d. 30 km/hr

Answer: d. 30 km/hr

Explanation:

D = S x T
∴ S =D; T =D
TS


Distance is same   
∴ D = D
∴ S1 x T1 = S2 x T2  
∴ 40 x6= ? x8---------> To convert minutes to hours, divide minutes by 60
6060
∴ ? = 30 km/hr (This should be the speed)

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