**TIME AND DISTANCE SHORTCUTS FOR QUANTITATIVE APTITUDE**

**1. Distance = Speed x Time**

**2. Time = Distance / Speed**

**3. Speed = Distance / Time**

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4. To convert speed in kmph to m/sec, multiply it with 5/18.

Eg 1: Express a speed of 72 km/hr in m/s?

Ans: 72 x (5/18) = 20 m/s

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5. To convert speed in m/sec to kmph , multiply it with 18/5.

Eg 2: Express a speed of 20 m/sec in km/hr?

Ans: 20 x (18 /5) = 72 km/hr

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6. If a body travels from point A to point B with a speed of 'p' and back to point A (from point B) with a speed of q, then the average speed of the body is:

= 2pq/(p+q).

Eg 3: A car covers a certain distance at a speed of 90 km/hr while going and returns to the starting point at a speed of 60 km/hr. Find the average speed of the car for the whole journey?

Ans: Average speed = (2 x 90 x 60)/ (60+90)

= 72 km/hr

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7. If a car does a journey in 'T' hrs, the first half at 'p' km/hr and the second half at 'q' km/hr. The total distance covered by the car:

= (2 x Time x p x q ) / (p + q).

Eg 4: A motorcar does a journey in 10 hrs, the first half at 21 kmph and the second half at 24 kmph. Find the distance?

Ans: Distance = (2 x 10 x 21 x 24) / (21+24)

= 10080 / 45

= 224 km.

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8. If a body covers part of the journey at speed p and the remaining part of the journey at a speed q and the distances of the two parts of the journey are in the ratio m : n, then the average speed for the entire journey is:

= (m+n) pq / (mq+np).

9. If a person travelling between two points reaches p hours late (If time is given in minutes, it should be converted in hrs by dividing it by 60) travelling at a speed of 'a' km/hr and reaches 'q' km/hr and reaches q hours early travelling at 'b' km/hr, the distance between the two points is:

= (ab/a-b)(p-q)

Eg 5: A person travelling at 6 kmph reaches his office 15 minutes late. Had he travelled at 8 kmph he would have been 25 minutes early. Find the distance the person has to travel to reach his office ?

Ans: Distance = (6 x 8 / 8-6) / ( 15/60 + 25/60)

= 16 km.

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10.If a person goes from 'A' to 'B' at a speed of 'p' kmph and returns at a speed of 'q' kmph and takes 'T' hours in all, then the distance between the A and B:

= Total time taken x (Product of the two Speeds / Addition of the two speeds)

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Eg 6: A boy goes to school at a speed of 3 kmph and returns to the village at a speed of 2 kmph. If he takes 5 hrs in all, what is the distance between the village and the school?

Ans: Let the required distance be x km.

Then time taken during the first journey = x/3 hr.

and time taken during the second journey = x/2 hr.

x/3 + x/2 = 5 => (2x + 3x) / 6 = 5

=> 5x = 30.

=> x = 6

Required distance = 6 km.

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Eg 7: Walking ¾ of his speed, a person is 10 min late to his office. Find his usual time to cover the distance?

Ans: Usual time = Late time / {1/ (3/4) - 1)

= 10 / (4/3 -1 )

= 10 / (1/3)

= 30 minutes.

Eg 8: Running 4/3 of his usual speed, a person improves his timing by 10 minutes. Find his usual timing by 10 minutes. Find his usual time to cover the distance?

Ans: Usual time = Improved time / { 1 - (1/ (3/4)}

= 10 / { 1- (3/4) }

= 40 minutes.

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11. A train travelling at a speed of 'S1' kmph leaves A at 't1' hrs. and another train travelling at speed 'q' kmph leaves A at 'S2' hrs in the same direction. Then the meeting point's distance from starting starting point:

= (S1 x S2 X Difference in time) / Difference in speed.

Eg 9: A train travelling 25 kmph leaves Delhi at 9 a.m. and another train travelling 35 kmph starts at 2 p.m. in the same direction. How many km from will they be together ?

Ans: Meeting point's distance from the starting point = [25 x 35 x (2p.m. - 9 a.m)] / (35 -25)

= (25 x 35x 5) / 10

= 4375 / 10

= 437.5 km .

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12. If two persons A and B start at the same time in opposite direction from two points and after passing each other they complete the journeys in 'a' and 'b' hrs respectively, then A's speed : B's speed = Square root of b : Square root of a.

Eg 10: A sets out to cycle from Delhi to Rohtak, and at the same time B starts from Rohtak to cycle to Delhi. After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively. At what rate does the B cycle if A cycles at 8 km per hour?

Ans: As per the above formula, the ratio of A's speed to B's speed = Square root of 4 4/5 / Square root of 3 1/3.

A's speed : B's speed = 6/5.

A's speed = 8 kmph

B's speed = (5/6) x 8

= 6 2/3 kmph.

13. If A travels certain distance at the rate of 'S1' kmph and B covers the same distance at the rate of 'S2' kmph and if one of them takes 't' minutes longer than the other, then:

Distance covered = {(S1 x S2) x Difference in time to cover the distance} / (S1-S2)

Note :- If speed is given kmph and time is given in minutes, then time is to be expressed in hrs. before solving the problem using this formula.

Eg 11: Two runners cover the same distance at the rate of 15 km and 16 km per hour respectively. Find the distance travelled when one takes 16 minutes longer than the other?

Ans: Distance travelled = {(15 x 16) x (16/60)} / (16-15)

= 64 km (TOP)