Harish on tour travels first 160 km at 64 km /hr and the next 160 km at 80 km /hr . The average speed of for the first 320 km of the tour is :
Answer: 71.11 km / hr
If a cyclist starts at 7 km/hr and he increases his speed in every 3 hours by 1 km/hr then the time taken by the cyclist to cover 113 km is:
a) 27/2 hours b) 20/3 hours c) 12 hours d) 13 hours
Answer : d) 13 hours
Solution :
Initial speed of the cyclist = 7km/hr.
Distance covered in 1st 3 hours = 7 x 3 = 21 km.
After increasing, 1km/hr for every 3 hours period,
Distance covered in 2nd 3 hours period = 8 x 3 = 24 km.
Distance covered in 3rd 3 hours period = 9 x 3 = 27 km.
Distance covered in 4th 3 hours period = 10 x 3 = 30 km.
Total distance covered = 21 + 24 + 27 + 30 = 102 km.
Remaining km to cover = 113 - 102 = 11 km.
Speed in 5th 3 hours period = 11 km/hr.
Time to cover 13 km at 11km/hr = 11/11 hours = 1 hour.
Now, the total time taken by him for 113 km = (3 + 3 + 3 + 3 + 1) = 13 hours.
A bike rider starts at 60 km/hr and he increases his speed in every 2 hours by 3 km/hr. Then the maximum distance covered by him in 24 hours is:
a) 1000km b) 918km c) 899 km d) none of these
Answer : b) 918 km.
Solution :
Speed of the rider = 60km/hr.
Distance covered in 1st 2 hours = 60 km.
He increased his speed in every 2 hours by 3 km/hr.
Distance covered in every 2 hours will be, 60, 63, 66,... upto 12 terms.(for 24 hours).
The above series is an A.P series;
Sum of first n terms = (n/2)(2a+(n-1)d)
Here, a = 60, d = 3 and n = 12.
Sum of first 12 terms = (12/2)(2(60)+(11)3) = 6(120 + 33) = 6(153) = 918.
Hence, he covers 918 km in 24 hours.
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Let the actual distance travelled be x km.
14x = 10x + 200
4x = 200
x = 50 km.
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Let speed of the car be x kmph.
Answer: 71.11 km / hr
If a cyclist starts at 7 km/hr and he increases his speed in every 3 hours by 1 km/hr then the time taken by the cyclist to cover 113 km is:
a) 27/2 hours b) 20/3 hours c) 12 hours d) 13 hours
Answer : d) 13 hours
Solution :
Initial speed of the cyclist = 7km/hr.
Distance covered in 1st 3 hours = 7 x 3 = 21 km.
After increasing, 1km/hr for every 3 hours period,
Distance covered in 2nd 3 hours period = 8 x 3 = 24 km.
Distance covered in 3rd 3 hours period = 9 x 3 = 27 km.
Distance covered in 4th 3 hours period = 10 x 3 = 30 km.
Total distance covered = 21 + 24 + 27 + 30 = 102 km.
Remaining km to cover = 113 - 102 = 11 km.
Speed in 5th 3 hours period = 11 km/hr.
Time to cover 13 km at 11km/hr = 11/11 hours = 1 hour.
Now, the total time taken by him for 113 km = (3 + 3 + 3 + 3 + 1) = 13 hours.
A bike rider starts at 60 km/hr and he increases his speed in every 2 hours by 3 km/hr. Then the maximum distance covered by him in 24 hours is:
a) 1000km b) 918km c) 899 km d) none of these
Answer : b) 918 km.
Solution :
Speed of the rider = 60km/hr.
Distance covered in 1st 2 hours = 60 km.
He increased his speed in every 2 hours by 3 km/hr.
Distance covered in every 2 hours will be, 60, 63, 66,... upto 12 terms.(for 24 hours).
The above series is an A.P series;
Sum of first n terms = (n/2)(2a+(n-1)d)
Here, a = 60, d = 3 and n = 12.
Sum of first 12 terms = (12/2)(2(60)+(11)3) = 6(120 + 33) = 6(153) = 918.
Hence, he covers 918 km in 24 hours.
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Let the actual distance travelled be x km.
| Then, | x | = | x + 20 |
| 10 | 14 |
14x = 10x + 200 4x = 200 x = 50 km.A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Let speed of the car be x kmph.
| Then, speed of the train = | 150 | x | = |  |
3 | x |  kmph. |
| 100 | 2 |
 |
75 | - | 75 | = | 125 |
| x | (3/2)x | 10 x 60 |
| |
75 | - | 50 | = | 5 |
| x | x | 24 |
| x = |
|
25 x24 | |
= 120 kmph. |
| 5 |
A car travelling with  of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
|
|
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: Let Abhay's speed be x km/hr.
6x = 30 x = 5 km/hr. |
