Hello bankersherald reader, Today we are going to talk about Quantitative aptitude part. All of you know Quantitative aptitude part is very important role of different type of competitive exam like banking sector exam, railways, ssc and other competitive exam.So guys today we are going to discussing about **Time, Speed and distance **question and basic formulas used in this section. So Bankers herald team are providing many solved and unsolved problem of Time , Speed and Distance.

**TIME, SPEED AND DISTANCE**

The major formulae used in TSD:

1.Distance (D)=Speed(S)x Time(T)

2.Speed (S)=Distance(D)/Time(T)

3.Time (T)=Distance (D)/Speed(S)

** Important Point Always Remember:**

- When distance is given in kilometer (Km), then speed should be used in Km/Hr and time in hours.
- When distance is given in meter, then speed should be used in m/sec and time in second
- Point number third , if speed is given Km/Hr, then in order to convert it , in m/sec, it is directly multiplied by 5/18

For example, 36Km/hr=36×5/18=10m/sec

4.If speed is given in m/sec, then in order to convert it, in Km/hr its directly multiplied by 18/5

For example, 20 m/sec=20×18/5=36Km/hr

**Example 1.Ram moves from A to B travelling a distance of 10 km in 4hr. What is ram’s Speed?**

**Answer- Distance (D)=10km**

** Total time =4hr**

** Speed= Distance (D)/Time (T)=10Km/4Hr=2.5Km/hr**

**Example 2.If ram moving at the speed of 2.5 Km/hr travels from Delhi to Agra in 1 day and total time take by ram 10 hr. Find the distance between Delhi to Agra.**

**Answer-Firstly Check unite**

** Then Apply Distance(D)=Speed x time**

** =2.5Km/hr x (1 day+10hr)**

** =2.5Km/hr x 34hr**

** =85Km**

**Relationship between Time, Speed and Distance:**

**1.You can see, speed is directly proportional to distance. So if twice the distance is traveled in same time, speed has become twice.**

**2.speed is inversely Proportional to time. So if speed x times, time taken to cover same distance will become 1/x times.**

**3.Distance is directly proportional to time taken , for example time taken at same speed becomes 1/x, it means distance also become 1/x th .**

**Note-All of point, try to avoid the use of equations. It will help you increase your speed tremendously.**

**Some solved question are in below**

**Example3.Ramesh sees Uma standing at a distance of 200 m from his position .He increase his speed by 50% and hence takes 20s now to reach her.**

**(a). If he travels at the original speed , how much time will be taken ?**

**(b).What was his original speed (in Km/hr)**

**(c).What is his new speed?**

**Explanation:**

**Part(a):Travelling at 1505of his original Speed(3/2)his original speed. Ramesh should take 2/3of the original time, 20s, thus his original time is 30 s.**

**Part(b):Speed=Distance/time**

** =200/30 m/s=20/3 x 18/5=24 Km/hr**

**Part(c):His new speed is 50 more =24 x 1.5**

** =36 Km/hr.**

**Relative Speed:**

**Case 1.If two persons are moving in opposite direction at speed V & v respectively.**

**The Relative Speed is given by Vr=V+v**

**Case2.It two persons are moving in same direction at speed V & v respectively.**

**The Relative Speed is given by Vr=|V-v|**

**Important Point Remember:**

- A man walking at S km/hr reaches his home t1 minutes late . if we walk V km/hr , he reaches there t2 minutes earlier then u always remember this formula

Distance(d) = {(S x V/V-S)X (t1+t2)/60 Km}

**Ex[4].A man walking at 2 km/hr , reaches his office 6 minutes late. if he walks 3 km/hr , he reaches there 6 minutes earlier . How far is the office from his house?**

Answer: Distance(D) =(3 X 2/3-2) X (6+6)/60

=6 X (12/60)=6/5 Km

**Ex[5].Two car cover the same distance at 15 km/hr and 16 km/hr respectively . Find the distance travelled by each , if one take 16 min longer then other. **

Answer: Suppose required distance x km.

x/15-x/16 =16/60

solve the above equation

we get , 16 x- 15 x =64

the required distance =64km

**Ex.6 Ram Covers a distance of 12 km in 45 minutes. if he covers half the distance in 2/3rd of the time then , what speed should be maintain to cover the remaining distance in the remaining time ?**

Answer:

Total distance =12 km

half distance = 6 km

Total time = 45mint

Time taken cover the half distance =45 x 2/3

=30 minutes

Time remaining =45-30 =15 minutes

**Ex[7].A person cover a distance of 120 km at 60 Km/hr and next 150 km at 50 Km/hr . What is hi average speed for his whole journey of 270 km ?**

Answer: Total time =120/60+150/50

=5Hr

Total distance =270

Average speed=270/5

=54 km/hr

**Ex[8].A and B are two different cities.Ram travels on car from A to B at a speed of 15 km/hr and returns back at the rate of 10 Km/hr.Find his average speed for the whole journey?**

Answer: you can use formula of average speed:

Average speed=2 u v/u+v

you get

2 x 15×10/25

=12 km/hr

**Ex[9].Ram travels 2/15 of his total journey by car .and 9/20 by cycle and the renaming 10 km on foot . What ihis total journey?**

Answer-Suppose total journey is x km

then, 2x/15+9x/20+10 =x

solved above equation we get x=24

total journey is 24