**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Speed, Distance and Time**

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The basic concept of speed, distance and ‘time’ are used in solving questions based on motion in straight line, relative motion, problems based on train, problem based .on boats, clocks, races etc.

To solve the problems from this chapter, basic concepts should be deeply understood, because of the diverse range of problems.

Mathematically, speed is the total distance covered by an object in unit time interval.

=> Distance (d) = Time (T) x Speed(S)

These are the basic formulae that can be useful for finding any of the variables on given conditions.

**Conversion of Units of Speed**

1 km/h = 5/18 m/s

1 m/s=18/5 km/h

**Example A bus is moving with a speed of 72 km/h and covers 440 m distance. Then, find the time taken to cover that distance.**

(a) 22 s

(b) 20 s

(c) 25 s

(d) 24 s

**Example A car covers a certain distance going at a speed of 60 km/h and returns to the starting point at a speed of 40 km/h. The average speed for the whole journey is SSC (1o+2) 2012**

(a) 48 km/h

(b) 50 km/h

(c) 45 km/h

(d) 40 km/h

**Some Useful Facts/****Formula**

- When a certain distance is covered at speed A and the same distance is covered at speed B, then the average speed during the whole journey is given by

2 AB/A + B

**Example Two men start together to walk a certain distance, one at 4 km/h and another at 3 km/h. The former arrives half an hour before the latter. Find the distance. SSC(10+2) 2012**

(a) 6 km

(b) 9 km

(c) 8 km

(d) 7 km

- If the new speed is a/b of the original speed, then the change in time taken to cover the same distance is given by change in time = (b/a-1) x Original time.
- If two persons A and B start at the same time from two points P and Q towards each other and after crossing they take T1h and T2h in reaching Q and P respectively,

then,A’s speed/B’s speed=√T2/√T1 - When two persons A and B travel from points P to Q, a distance of D with speeds a and b, respectively and B reaches Q first, returns immediately and meets A at R,

then

Distance travelled by A (from points P to R) = 2 x D(a/a+b)

Distance travelled by B (PQ + QR) = 2xD(b/a+b)

**Example Sonu and Monu travel from points P to Q, a distance of 42 km, at 6 km/h and 8 km/h, respectively. Monu reaches Q first and returns immediately and meets Sonu at R. Find the distance from points P to R.**

(a) 32 km

(b) 36 km

(c) 40 km

(d) 38 km

- Two persons A and B start running at the same time in opposite directions from two points and after passing each other they complete their journeys in x h and y h, respectively. Then,

A’s speed : B’s speed = √y : √x

**Example A man sets out to cycle from points P to Q and at the same time another man starts to cycle from points Q to P. After passing each other, they complete their journeys in 9 h and 4 h, respectively. Find the ratio of speeds of 1st man to that of 2nd man.**

(a) 3 : 2

(b) 4 : 3

(c) 3 : 4

(d) 2 : 3

**Concept of Trains**

A train is said to have crossed an object (stationary or moving) only when the last coach (end) of the train crosses the object completely. It implies that the total length of the train has crossed the total length of the object.

Thus, distance covered by the train = Length of train + Length of object

**Note** The difference between simple problems and train based problems is only that in train based problems, the length of train is also considered.

**Example Let the two trains are moving in the same direction with speed of 50 km/h and 75 km/h, respectively. If the faster moving train crosses a person who is sitting in second train in 36 s, then what is the length of faster moving train?**

(a) 250 m

(b) 225 m

(c) 150 m

(d) 175 m

**Example A train, 300 m long, passed a man, walking line in the same direction at the rate of 3 km/h 33 s. The speed of the train is SSC(10+2)2010**

(a) 30 km/h

(b) 32 km/h

(c) 32 8/11km/h

(d) 35 8/11km/h

**Concept of Boats and Streams**

In these types of problems, boats and streams are considered as single system. Here, also same formula of speed, time and distance applied.

**Terminology**

**Speed of Boat** If the speed of a boat is given, then that particular speed is the speed of boat in still water.

**Upstream Motion** If the boat (or swimmer) moves against along the the stream i.e., the direction opposite to that of the stream is called upstream.

**Downstream Motion** If the boat (or swimmer) moves with the stream i.e., along the direction of the stream it is called downstream.

**Some Points Regarding Speed of Boat and Stream**

If the speed of a boat in still water is x and speed of the stream is y, then

• Speed downstream = (x + y)

• Speed upstream = (x – y)

• Speed of boat in still water (x) = 1/2

(Speed downstream + Speed upstream)

• Speed of stream (y) = 1/2

(Speed downstream – Speed upstream)

**Example The speed of a stream is 3 km/h and the speed of a man is still water is 5 km/h. The time taken by the man to swim 26 km downstream is SSC (10 + 2) 2012**

(a)5 1/5h

(b)8 2/3h

(c)3 1/4h

(d)13h

**Reference Corner**

**1. A missile travels at 1350 km/h. How many metres does it travel in one second? SSC (10+2) 2017**

(a) 369 m

(b)375m

(c) 356 m

(d) 337 m

**2. A student goes to school at the rate of 2 1/2 km/h and reaches 6 min late. If he travels at the speed of 3 km/h, he is 10 min early. What is the distance to the school? SSC (10 + 2) 2015**

(a) 4 km

(b) 3 1/4 km

(c) 1 km

(d) 3 1/2 km

**3. A car travels at a speed of 60 km/h and covers a particular distance in 1 h. How long will it take for another car to cover the same distance at 40 km/h? SSC (10 + 2) 2014**

(a)3/2h

(b)1h

(c)5/2h

(d) 2h

**4.Two trains, of same length, are running in parallel tracks in opposite directions with speed 65 km/h and 85 km/h respectively. They cross each other in 6s. The length of each train is SSC (10+2) 2013**

(a) 100 m

(b) 115 m

(c) 125m

(d) 150 m

**Practice Exercise**

**1. Arjun walks from his house at 2 1/2 km/ h and reaches his school late by 6 min. Next day, he increases his speed by 1 km/h and reaches 6 min before school time. How far is the school from his house?**

(a) 5/4 km

(b) 7/4 km

(c) 9/4 km

(d) 11/4 km

**2.Walking with 3/4 of his usual speed Nihal covers a certain distance in 2 h more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with usual speed is**

(a) 4 1/2 h

(b) 5 1/2 h

(c) 5 h

(d) 6 h

**3. The distance between two stations A and B is 220 km. A train leaves A towards B at 80 km/h. After half an hour, another train leaves B towards A at 100 km/h. The distance of the point, where the two trains meet, from A is**

(a) 120 km

(b) 130 km

(c) 140 km

(d) 150 km

**4.A man travels 35 km partly at 4 km/h and at 5 km/h. If he covers former distance at 5 km/h and later distance at 4 km/h, he could cover 2 km more in the same time: The time taken to cover the whole distance at original rate**

(a) 9 h

(b) 7 h

(c) 8 h

(d)6 1/2 h

**5. Sujal covers a distance in 40 min, if he drives at a speed of 60 km/h on an average. Find the speed at which he must drive at to reduce the time of the journey by 25%?**

(a) 60 km/h

(b) 70 km/h

(c) 75 km/h

(d) 80 km/h

**6. A plane left half an hour later than the scheduled time and in order to reach its destination 1500 km away in time, it had to increase its speed by 33.33% over its usual speed. Find its increased speed.**

(a) 250 km/h

(b) 500 km/h

(c) 750 km/h

(d) 1000 km/h

**7. A motorboat went downstream for 28 km and immediately returned. It took the boat twice as long to make the return trip. If the speed of the river flower twice is high, the trip downstream and back would take 672 min. Find the speed of the boat in still water and the speed of the river flow.**

(a) 9 km/h, 3 km/h

(b) 9 km/h, 6 km/h

(c) 8 km/h, 2 km/h

(d) 12 km/h, 3 km/h

**8. In a race of 600 m, Anil beats Vimal by 60 m and in a race of 500 m. Vimal beats Aman by 25 m. By how many metres will Anil beat Amain in a 400 m race?**

(a) 48 m

(b) 52 m

(c) 56 m

(d) 58 m

**9. Two horses started simultaneously towards each other and meet each other 3 h 20 min later. How much time will it take the slower horse to cover the whole distance if the first arrived at the place of departure of the record 5 h later than, the second arrived at the point of departure of the first?**

(a) 10 h

(b) 5 h

(c) 15 h

(d) 6 h

**10. The difference between the times taken by two buses to travel a distance of 350 km is 2 h 20 min. If the difference between their speeds is 5 km/h, find the slower speed.**

(a) 35 km/h

(b) 30 km/h

(c) 25 km/h

(d) 20 km/h

**11. One bad day, at 7 : 00 am I started on my bike at the speed of 36 km/h to meet one of my relatives. After, I had travelled some distance, my bike went out of order and I had to stop. After resting for 35 min, I returned home on foot at a speed of 14 km/h and reached home at 1 : 00 pm. Find the distance from my house at which my bike broke down.**

(a) 54 km

(b) 63 km

(c) 72 km

(d) None of these

**12. X and Y start walking towards each other at 8 : 00 am at the speeds of 3 km/h and 4 km/h respectively. They were initially 17.5 km apart. At what time do they meet?**

(a) 10 : 30 am

(b)10 : 30 pm

(c) 11 : 30 am

(d) 11: 30 pm

**13. A train P starts from Mokama at 5 : 00 pm and reaches Hazipur at 6 : 00 pm. An another train Q starts from Hazipur at 5 : 00 pm and reaches Mokama at 6 : 30 pm. At what time, two trains will cross each other?**

(a) 5 :36 pm

(b) 4:36 pm

(c) 6 : 00 pm

(d) 7 : 00 pm

**14. The distance travelled by a train is 1830 km. The speed of the train is one more than twice the time taken to travel the distance what will be the respective ratio of the speed of the train and time taken to travel?**

(a) 30:61

(b) 61:30

(c) 25:51

(d) 51:25

**15. A boatman takes twice a long to row a distance against the stream as to row the same distance with the stream. Find the ratio of speeds of the boat in still water and the stream.**

(a) 2 :1

(b) 3 :1

(c) 1 : 2

(d) 1: 3

**16. The average speed of a car is 75 km/h. The driver first decrease its average speed by 40% and then increases it by 50%. What is the new average speed now?**

(a) 67.5 km/h

(b) 60 km/h

(c) 90 km/h

(d) 60.5 km/h

**17. A car driver covers a distance between two cities at a speed of 60 km/h and on the return his speed is 40 km/h. He goes again from the Ist to the IInd city at twice that original speed and returns at half the original return speed. Find his average speed for the entire journey.**

(a) 55 km/h

(b) 50 km/h

(c) 48 km/h

(d) 40 km/h

**18. The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for 2 h on reaching the destination. The total time taken to complete to and from journey is 32 h, covering a distance of 1600 km. Find the speed of the train the onward journey.**

(a) 56.25 km/h

(b) 60 km/h

(c) 66.50 km/h

(d) 67 km/h

**Answers**

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