Question 1

How long will a boy take to run round a square field of side 35 meters, If he runs at the rate of 9 km/hr?

Accepted Answer

Speed = 9 km/hr = 9 x (5/18) m/sec = 5/2 m/sec Distance = (35 x 4) m = 140 m. Time taken = 140 x (2/5) sec= 56 sec

Question 2

A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is

Accepted Answer

Time taken in walking both ways = 7 hours 45 minutes --------(i) Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii) By equation (ii)*2 -(i), we have Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes = 4 hours 45 minutes

Question 3

A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is

Accepted Answer

speed = (5x5/18)m/sec = 25/18 m/sec. Distance covered in 15 minutes = (25/18 x 15 x 60)m = 1250 m.

Question 4

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is

Accepted Answer

Total time taken = (160/64 + 160/8)hrs = 9/2 hrs. Average speed = (320 x 2/9) km.hr = 71.11 km/hr.

Question 5

The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?

Accepted Answer

Suppose they meet x hrs after 8 a.m then, [Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 330. Therefore, 60x + 75(x-1) = 330. => x=3. So,they meet at (8+3) i.e, 11a.m.

Question 6

Akash leaves mumbai at 6 am and reaches Bangalore at 10 am . Prakash leaves Bangalore at 8 am and reaches Mumbai at 11:30 am. At what time do they cross each other?

Accepted Answer

Time taken by Akash = 4 h Time taken by Prakash = 3.5 h For your convenience take the product of times taken by both as a distance. Then the distance = 14km Since, Akash covers half of the distance in 2 hours(i.e at 8 am) Now, the rest half (i.e 7 km) will be coverd by both prakash and akash Time taken by them = 7/7.5 = 56 min Thus , they will cross each other at 8 : 56am.

Question 7

In a one km race A gives B a start of 100m and in a one km race B gives a start of 80 m to C. In a 1 km race who will win and by how much distance from the worst performer between two losers?

Accepted Answer

Ratio of speeds of A:B = 1000:900 = 100:90 Ratio of speeds of B:C = 1000:920 = 100:92 Therefore, when A moves 1000m, B moves 900 m and when B moves 900m, C moves 828m Since, C moves 8 % less than B at the same time. Thus, C is the worst performer and A will win by him by 172 m

Question 8

A train overtakes two girls who are walking in the opposite direction in which the train is going at the rate of 3 km/h and 6km/h and passes them completely in 36 seconds and 30 seconds respectively. The length of the train is:

Accepted Answer

Let the length of the train e x meter, and let the speed of train be y km/h, then x = y + 3 × 5 18 × 36 --------(1) and x = y + 6 × 5 18 × 30 ---------(2) From eq (1) and (2), we get y = 12 km/h Therefore, x = ( y + 3 ) × 5 18 × 36 => x= 150 m

Question 9

The distance of the college and home of Rajeev is 80km. One day he was late by 1 hour than the normal time to leave for the college, so he increased his speed by 4km/h and thus he reached to college at the normal time. What is the changed (or increa…

Accepted Answer

Let the normal speed be x km/h, then 80 x - 80 ( x + 4 ) = 1 ⇒ x 2 + 4 x - 320 = 0 ⇒ x (x + 20) - 16 (x + 20) = 0 (x + 20 ) (x - 16) =0 x = 16 km/h Therefore (x + 4) = 20 km/h Therefore increased speed = 20 km/h

Question 10

A train with 120 wagons crosses Arun who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the Arun ( he is riding on the horse) before it starts overtaking the Sriram( who is also riding o…

Accepted Answer

Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then L R - A = 36 ---------- (i) and L R + K = 24 ---------(ii) From eq.(i) and (ii) 3(R - A ) = 2 (R + K) ⇒ R = 3A + 2K In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram = 1800 ( R - A) - 24 ( A + K) Time required = 1800 ( R - A ) - 24 ( A + K ) ( A + K ) = (3600 - 24) = 3576 s

Question 11

The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is

Accepted Answer

The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.

Question 12

The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?

Accepted Answer

Let the speeds of two trains be 7X and 8X km/hr. 8x = 400/4 => x= 12.5 km/hrX=4004=>X=12.5Km/hr So speed of first train is 12.5*7 = 87.5 km/hr

Question 13

Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once throu…

Accepted Answer

Amy can travel clockwise or anticlockwise on the diagram. Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes. Similarly, anticlockwise she has four different routes. Total routes = 8

Question 14

A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.

Accepted Answer

We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance. Lets solve it. Time = 50/60 hr = 5/6 hr Speed = 48 mph Distance = S*T = 48 * 5/6 = 40 km New time will be 40 minutes so, Time = 40/60 hr = 2/3 hr Now we know, Speed = Distance/Time New speed = 40*3/2 kmph = 60kmph

Question 15

A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house ?

Accepted Answer

Let distance = x km. Time taken at 3 kmph : dist/speed = x/3 = 20 min late. time taken at 4 kmph : x/4 = 30 min earlier difference between time taken : 30-(-20) = 50 mins = 50/60 hours. x/3- x/4 = 50/60 x/12 = 5/6 x = 10 km.

Question 16

A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

Accepted Answer

Number of gaps between 41 poles = 40 So total distance between 41 poles = 40*50 = 2000 meter = 2 km In 1 minute train is moving 2 km/minute. Speed in hour = 2*60 = 120 km/hour

Question 17

If Deepesh had walked 20 km/h faster he woulh have saved 1 hour in the distance of 60km. what is the usual speed of Deepesh?

Accepted Answer

Let the original speed be x km/h, then 600 x - 600 x + 20 = 1 ⇒ 600 x + 20 - x x x + 20 = 1 ⇒ x 2 + 120 x - 12000 = 0 ⇒ x - 120 x - 100 = 0 Therefore, original speed = 100km/h

Question 18

A man covers half of his journey by train at 60 km/hr, half of the remaining by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey?

Accepted Answer

Let the total distance of the journey of a man = d kms Now, the average speed of the entire journey = d d 120 + d 120 + d 40 = 24 kmph.

Question 19

A and B runs around a circular track. A beats B by one round or 10 minutes. In this race, they had completed 4 rounds. If the race was only of one round, find the A's time over the course:

Accepted Answer

B runs around the track in 10 min. i.e , Speed of B = 10 min per round Therefore, A beats B by 1 round Time taken by A to complete 4 rounds = Time taken by B to complete 3 rounds = 30 min Therefore, A's speed = 30/4 min per round = 7.5 min per round Hence, if the race is only of one round A's time over the course = 7 min 30 sec

Question 20

A Person X started at 3 hours earlier at 40km/h from a place P, then another person Y followed him at 60km/h. Started his journey at 3 O'clock, afternoon. What is the diference in time when X was30 km ahead of Y and when Y was 30 km ahead of X?

Accepted Answer

Time ( when X was 30 km ahead of Y) = (120-30)/20 =4.5h Time ( when Y was 30 km ahead of X) = (120+30)/20 = 7.5 h Thus, required difference in time = 3h

Time and Distance Questions