Aptitude_Q&A_01


Useful Facts:
I) Speed (kmph), is distance (km) travelled in unit time (hr)..

II) For 2 trips of equal distances,
Speeds and Times are in opposite (inverse) ratios.


11. Ram cycles 600m in 5 minutes. What is his speed in kmph?
 
 Solution:
12 x 5 = 60 min. Distance is 12 x 600m = 7200 m = 7.2 km.
So speed is 7.2 kmph.
 
Better: (Avoiding multiplication by 12)
 
  In 5 min., 600m; in 10 min., 1200m; in 60 min. 7200m.
So speed is 7.2 kmph.


12. An aeroplane flies a certain distance at 240 kmph in 5 hrs.
At what speed the plane should fly to cover the same distance in
1 hours?
 
 Solution:
Ratio of time is 3 : 1
Distance is same.
So, ratio of speed is the opposite of ratio of time and so is 1 : 3.
So speed is 240 x 3 = 720 kmph.


13. If a person walks at 14 km/h instead of 10 km/h, he would have walked 20 km more. What is the actual distance travelled by him?
 
 Solution:
4km more every hour; 20km in 5 hrs; so he walked for 5 hours.
Actual distance walked is 10 x 5 = 50 km.


14. 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. What is the speed of the car?
 
 Solution:
Distance is same; 75kms.
Speed ratio is Car : Train = 2 : 3.
So time ratio is Car : Train = 3 : 2.

The difference 1 part is 12.5 minutes.
So car's time is 3 parts, which is 37.5 min.
In 37.5 min, Car travels 75 kms;
In 60 min, Car travels 120 kms. (Note 75 is double 37.5!)
So Car's speed is 120 kmph. (Double of 60!)


15. 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?
 
 Solution:
Bus normally travels 54km in 1 hour.
With stoppages, it travels only 45km in 1 hour.
It stops for the equivalent time for 9km by normal speed.
This is one-sixth of 1 hour (time for 54km) = 10 min.
 
Or:
 
  Speed ratio = 54 : 45 = 6 : 5.
A sixth of speed implies a sixth of the distance is lost.
i.e. a sixth of the time (60 min) is lost
So stops for a sixth of time, 1 hr, and this is 10 min.