Question 1

Starting from his house, one day a student walks at a speed of 3 km/h and reaches his school 5 min late. Next day he increases his speed by 1 km/h and reaches the school 3 min early. How far is the school from his house?

Accepted Answer

Let the distance be D km Difference in timings = 8 min = 8/60 h = 2/15 h ∴ D/3 - D/4 = 2/15 ⇒ D/12 = 2/15 ⇒ D = 2 x 12/15 = 1.6 km

Question 2

A thief running at 8 km/h is chased by a policeman whose speed is 10 km/h. If the thief is 100 m ahead of the policeman, then the time required for the policeman to catch the thief will be

Accepted Answer

Relative speed of policeman with thief = (10 - 8) = 2 km/h Now, time taken to cover 100 m with speed of 2 km/h or 2000 m/h Now, Speed = Distance / Time ∴ Time = D/S = 100/2000 = 1/20 h or 60/20 min = 3 min

Question 3

A person can row 7 1/ 2 km/h in still water. It takes him twice as long to row up a distance as to row down the same distance. Find the speed of the stream?

Accepted Answer

Speed upstream + Speed downstream = 2 x 71/2 = 15 km/h Since, the time taken is in the ratio 2 : 1 hence the speed will be in the ratio 1 : 2 ∴ Speed upstream = (1/3) x 15 = 5 km/h and speed downstream = (2/3) x 15 = 10 km/h ∴ Speed of stream = (10 - 5)/2 = 2.5 km/h

Question 4

A streamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h , find the distance between the two ports?

Accepted Answer

Let the distance between the two ports = L km Then, speed downstream = L/4 and speed upstream = L/5 ∴ Speed of the stream = 1/2(L/4 - L/5) ⇒ 1/2[(5L - 4L)/20] = 2 ⇒ L = 80 km

Question 5

The current of a stream runs at 1 km/h. A motorboat goes 35 km upstream and back again at the starting point in 12 h. What is the speed of motorboat in still water?

Accepted Answer

Let the speed of boat in still water be V km/h. Then, 35/(V - 1) + 35/(V + 1) = 12 ⇒ 35(V + 1 + V - 1) = 12(V2 - 1) ⇒ 6V2 - 35V - 6 = 0 ⇒ (V - 6)(6V + 1) = 0 ⇒ V = 6 (V = - 1/6 is not possible) So, speed of boat in still water is 6 km/h.

Question 6

The speed of a motorboat is 30 km/h. It starts from Mumbai at 6 am and reaches Goa at 8 am. Same day, it starts from Goa at 12 pm and reaches Mumbai at 4 pm. Find the the speed of stream.

Accepted Answer

Clearly, motorboat takes 2 h go from Mumbai to Goa and 4 h to go from Goa to Mumbai. i.e., Time taken to row upstream = 2 x Time taken to row downstream ∴ n = 2 Let the speed of stream be V km/h. According to the formula, Speed of boat = V(n + 1)/(n - 1) ⇒ 30 = V(2 + 1)/(2 - 1) ∴ V = 30/3 = 10 km/h

Question 7

At his usual rowing speed, Kapil can travel 12 miles downstream in a certain river in 6 h less than he takes to travel the same distance upstream. But, If he could double his usual rowing speed for his 24 miles round trip, the downstream 12 miles wo…

Accepted Answer

Let speed of Kapil in still water = x and speed of the current= y ∴ Speed upstream = (x - y) and speed downstream = (x + y) According to the question, 12/(x - y) - 12/(x + y) = 6 ⇒ 6(x2 - y2) = 24y ⇒ x2 - y2 = 4y ⇒ x2 = 4y + y2 ....(i) Again, 12/(2x - y) - 12/(2x + y) = 1 ⇒ 4x2 - y2 = 24y ⇒ x2 = (24y + y2)/4 ....(ii) From Eqs. (i) and (ii), we get 4y + y2 = (24y + y2)/4 ⇒ 16y +4y2 = 24y + y2 ⇒ 3y2 = 8y ∴ y = 8/3 = 22/3 mile/h

Question 8

A person riding a bike crosses a bridge with a speed of 54 km/h. What is the length of the bridge, if he takes 4 min to cross the bridge?

Accepted Answer

Length of the bridge = Distance travelled by the person in 4 min = Speed x Time Speed = 54 km/h = 54 x (5/18) = 3 x 5 = 15 m/s Time = 4 min = 4 x 60 = 240 s ∴ Required length = 15 x 240 = 3600 m

Question 9

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.

Accepted Answer

Let total distance = x km According to the question, x/3 - x/4 = 1/2; ⇒ x/12 = 1/2 ∴ x = 6 km

Question 10

Aashutosh can cover a certain distance in 84 min by covering 2/3rd of distance at 4 km/h and the rest at 5 km/h. Find the total distance.

Accepted Answer

Let the total distance = L Then, according to the question, (2L/3)/ 4 + (1 - 2/3)L/5 = 84/60 ⇒ 2L/12 + L/15 = 84/60 ⇒ L/6 + L/15 = 84/60 ⇒ 5L + 2L = 42 ⇒ 7L = 42 ∴ L = 42/7 = 6 km

Question 11

A bullock cart has to cover a distance of 80 km in 10 h. If it covers half of the journey in 3/5th time, what should be its speed to cover the remaining distance in the left time?

Accepted Answer

Total distance to covered in 10 h = 80 km But it covers 40 km in 3/5th of time, i.e, 40 km in 6 h. ∴ Required time = 10 - 6 = 4 h And remaining distance = 40 km Thus, required speed = 40/4 =10 km/h

Question 12

Rani covers a certain distance by car driving at 5 km/h and returns the starting point riding on a scooter at 2 km/h. Find her average speed for the whole journey.

Accepted Answer

According to the formula, Average speed = 2AB/(A + B) Here, A = 5 km/h, and B = 2 km/h ∴ Required average speed = (2 x 5 x 2)/7 = 20/7 = 26/7 km/h

Question 13

A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?

Accepted Answer

Given that, W + D = 6 ...(i) [ w = Time taken while walking and D = Time taken while driving ] From Eq. (i) 5 +D = 6 ⇒ D = 1 2D = 2 x 1 = 2 ∴ He will take 2 h to drive both ways.

Question 14

Two men A and B travel from point P to Q, a distance of 84 km at 12 km/h and 16 km/h, respectively. B reaches Q and returns immediately and meet A at R. Find the distance form P to R.

Accepted Answer

Given, D = 84 km, a = 12 km/h and b = 16 km/ h According to the formula Distance traveled by A = PR = 2D x a/(a + b) = 2 x 84 x 12/(12 + 16) = (2 x 84 x 12)/28 = 2 x 6 x 6 = 72 km

Question 15

A thief is spotted by a policeman from a distance of 200 m. When the policeman starts chasing, the thief also starts running. If the speed of the thief be 16 km/h and that of the policeman be 20 km/h, how far the thief will have run before he is ove…

Accepted Answer

Relative speed of policeman = ( 20 - 16 ) x 5/18 = 10/9 m/s To catch the thief, the policeman in has to gain 200 m = 200 x 9/10 = 180 s Actual distance covered by policeman in 180 s = 180 x 50/9 = 100 m ∴ Distance covered by the thief = 1000 - 200 = 800m

Question 16

A person sets out to cycle from A to B and at the same time another person starts from B to A. After passing each other, they complete their journeys in 16 h and 25 h, respectively. Find the ratio of speeds of the 1st man to that of the 2 nd man.

Accepted Answer

Given, x = 16 and Y = 25 According to the formula, 1st man's speed : 2nd man's speed = √ y : √ x = √ 25 : √ 16 = 5 : 4

Question 17

A certain distance is covered at a certain speed. If half of this distance is covered in 4 times of the time, then find the ratio of the two speeds.?

Accepted Answer

Let L km is covered in T h. Then, first speed = L/T km/h Again, L/2 km is covered in 4T h. ∴ New speed = (L/2 x 1/4T ) = (L/8T) km/ h Ratio of speed = L/T : L/8T = 1 : 1/8 = 8 : 1

Question 18

A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. Find his average speed.

Accepted Answer

Given, A = 6 km/h, B = 3 km/ h According to the formula, Average speed = 2AB/(A + B) ∴ Required average speed = 2 x 6 x 3/(6 + 3) = 36/9 = 4 km/h

Question 19

A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 56 min will be covered by A in?

Accepted Answer

Let time taken by A = Y Let speed of C = x Then, speed of B = 3x ∴ speed of A = 6x Now, ratio of speeds of A and C = Ratio of time taken by C and A 6x : x = 56 : y ⇒ 6x/x = 56/y ∴ y = 56/6 = 92/6 = 91/3 min

Question 20

The ratio of the speeds of A and B is 3 : 4. A takes 20 min more than the time taken by B to reach a particular place. Find the time taken by A and B, respectively to reach that place.

Accepted Answer

Ratio of speeds of A and B = 3 : 4 ∴ Ratio of time taken = 4 : 3 Let time taken by A and B be 4k and 3k, respectively. Then, according to the question, 4k - 3k = 20 ⇒ k = 20 Hence, time taken by A = 4 x 20 = 80 min And time taken by B = 3 x 20 = 60 min

Time and Distance Questions