Become a master of ‘time and distance’ in aptitude section

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Distance topic. 1. In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 […]

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and solutions on the Time and Distance topic.

1. In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time?

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Solution:

The time is same for both A and B.
Let Time = x hrs
Distance for ‘A’ = 500 m, Speed of A = 500/x km/hr

Distance for ‘B’ = 500 – ( 45 35) = 420 m Speed of B = 420/x km/hr
The ratio of speeds of A and B is A : B = 500/x : 420/x = 25 : 21
2. In a 500 m race, A reaches the final point in 28s and B reaches in 35s. By how much distance does A beats B?

Solution:

Here, we have to find the distance covered by B, after A has finished the race i.e. distance covered by B in (35 – 28 = 7s).
Distance = 500/35 × 7 = 100 m

A beats B by 100 m

3. In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?
Solution:
If ‘A’ covers 10 km, then ‘B’ covers 9 km in same time.

So the ratio of Speeds of A and B is A:B = 10:9

Similarly the ratio of Speeds of B and C is B:C = 10:9

So the ratio of Speeds of A, B and C is A:B:C = 100:90:81

If ‘A’ covers 100 m then ‘C’ covers 81 m in same time
If ‘A’ covers 10,000 m (10 km) then ‘C’ covers 8100 m in same time.
Therefore A would beat C by 1900 m.
4. A car covers a distance of 480 km in 6 hours and a bike covers a same distance in 8 hours. Find the ratio of speeds of car and bike?

Solution:

Speed of Car: Speed of Bike = 480/6 ∶ 480/8 = 80 : 60 = 4 : 3
5. The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. What was the total distance travelled in 12 hours?

Solution:

The total distance covered by car in 12 hours = 35 37 39 …………12 times
It is in Arithmetic Progression
Here the first term ‘ a’ = 35
Number of terms ‘n’ = 12
Common difference ‘d’ = 2
The sum of ‘n’ terms in AP = n/2 {2a (n-1)d}
Required Distance = 12/2 {2 ×35 11×2} = 6 (70 22) = 6 × 92 = 552 km
6. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

Solution:

The relative speed of the policeman and thief = 11 – 10 = 1 km/hr
Distance covered in 6 minutes = T × S = (6/60) ×1 = 1/10 km = 100 m

Therefore, the distance between policeman and thief = 200 = 100 = 100 m

Banda Ravipal Reddy

Director, SIGMA
Sai Institute of General Mental Ability
Hyderabad