# Time and Distance Problems Syllabus Notes 2022 Download Study Materials BOOK PDF

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Time and distance – Easy

1. If a car runs at 45km/hr, it reaches its destination late by 10 min but if runs at 60km/hr it is late by 4min. What is the correct time for the journey?

A. 24min

B. 14min

C. 32min

D. 20min

E. 46min

Correct option is : B

Solution:

Distance = diff in time *(S1*S2)/S1-S2

D=[10-4]/60hr * (45*60)/[60-45] = 6/60 * 45*60/15

==>18km

time T=D/S(take any one of the speed. 18/45 =2/5hrs = 2/5*60=24min

then correct time is 24-10=14mins.

1. A truck running from a city at a speed of 40 km/hr and the speed of the truck was increased by 2 km/hr at the end of every hour. Find the total distance covered by the truck in the first 5 hours of the journey.

A. 180 km

B. 120 km

C. 220 km

D. 90 km

E. 105 km

Correct option is : B

Solution:

The total distance covered by the truck in the first 5 hours

= 40 + 42 + 44 + 46 + 48

sum of five terms in AP whose first term is 40 and last term is 48

= 5/2 [40 + 48] = 220 km.

1. Two persons start running simultaneously around a rectangular track of length 700 m from the same point at speeds of 45 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?

A. 50 sec.

B. 42 sec.

C. 25 sec.

D. 36 sec.

E. 40 sec.

Correct option is : D

Solution:

Time taken to meet for the first time = length of the track/ relative speed

= 700 / (45 + 25)

= (700*18)/(70*5) = 36 sec.

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Time and distance – Moderate

1. A car traveled 80% of the distance from town A to B by traveling at T hours at an average speed of V km/h. The car travels at an average speed of S km/h for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A. 12VS/(9V+S)

B. 5VS/(4S+V)

C. VT/3S

D. 9VS/(4S+V)km/h

E. None of these

Correct option : B

Solution:

80 % of the distance = VT km

Total distance =  100 =  VT

Remaining distance =  VT – VT  =  VT

Remaining time =  hours

Total time = T +

Average speed  =

=  =  km/hr

Difference = 6-4 = 2 hours

1. Two places A and B are at a distance of 480Km. Sita started from A towards B at the speed of 40Kmph. After 2 hours Gita started from B towards A at speed of 60 Kmph. They meet at a Place C then what is the difference between the time taken by them to reach their destinations from Place C?

A. 1 hour

B. 2 hours

C. 3 hours

D. 4 hours

E. Cannot be determined

Correct option is : B

Solution:

t*40+ (t-2)*60 = 480

t=6

From Place C to A = C to B = 240

Then time taken by Sita = 6hours and GIta = 4 hours

1. The distance between two places A and B is 370 km. the 1st car departs from place A to B, at a speed of 80 kmph at 10 am and 2nd car departs from place B to A at a speed of 50 kmph at 1 pm. At what time both cars meet each other?

A. 2 : 30 pm

B. 2 : 00 pm

C. 2 : 10 pm

D. 2 : 20 pm

E. None of these

Correct option is : B

Solution:

Total distance = 370 km

Now, the distance covered by first car in (10 am to 1 pm= 3 hours)

= 80 × 3 = 240 km

Remaining distance = 370 – 240 = 130 km

Relative speed = 80 + 50 = 130 kmph

So, they meet 60 mins after 1 pm.

So, reqd answer = 2 : 00 pm

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Time and distance – Hard

1. Two buses start at same time from Chennai and Bangalore, which are 250km apart. If the two buses travel towards each other, they meet after 1hr and if they travel in same direction they meet after 5hrs. What is the speed of the bus starts from Chennai if it is know that the one which started from Chennai has more speed than the other one?

A. 150km/hr

B. 100km/hr

C. 45km/hr

D. 80km/hr

E. 120km/hr

Correct option is : A

Solution:

S=D/T Here we have two speeds.

We get 2 equations as.

250/1hr = C+B—1 (Travelling in opposite direction, speed must be added ie C+B) 250/5hr = C-B—2 (Travelling in same direction, speed to be subtracted. ie C-B)

solving 2 eqn C=150km/hr.

1. P, Q & R participated in a race. P covers the same distance in 49 steps, as Q covers in 50 steps and R in 51 steps. P takes 10 steps in the same time as Q takes 9 steps and R takes 8 steps. Who is the winner of the race?

A. P

B. Q

C. R

D. Can’t be determined

E. None of these

Correct option is : A

Solution:

Distance=> P*49 = Q*50 = R*51

P= Distance/49, Q= Distance/50, R= Distance/51

Time => P*10 = Q*9 = R*8

P = Time/10, Q = Time/9, R= Time/8

P’s speed = (Distance/49)/(Time/10) = 10/49

Same like that,

The ratio of speeds of P, Q, R = (10/49) : (9/50) : (8/51)

Hence, P is the fastest.

1. There are three athletes A, B and C at a same point. A starts running from a point at a speed of 40 m/min. After 5 minutes, B starts running after A with a speed of 50 m/min. Simultaneously, C also starts running after A at 60 m/min. What distance has C covered (in m) when he catches A?

A. 500/3

B. 1300/3

C. 700/3

D. 600

E. None of these

Correct option is : D

Solution:

When B started, A is ahead by 40 × 5 = 200 m
But C will catch A before the B as he is faster than the B.
Since A and C run in the same direction, relative speed of C = 60 − 40 = 20 m/min

Distance actually covered by C in this duration = 10 × 60 = 600 m