# Time and Distance

Directions (Qs. 1 - 8): Read the following questions carefully and choose the right answer.

1. Anju starts walking from U towards V with speed 5 km/hr and Rani starts on her scooty from V towards U with the speed 45 km/hr. In how much time do they meet if both starts at 6 AM and distance between U and V is 320 km?

A) 1:35 PM         B) 12:24 PM          C) 12:36 PM        D) 11:45 AM          E) 2:24 PM

Explanation: Speed of Anju = 5 kmph,

speed of Rani = 45 kmph

Time taken = 320 / 50 = 6.4 hours They started at 6 AM, so they will meet at 12:24 PM

Ans:B

2. Ashwini and Alpana run a 14.4 km race on a circular track of circumference 960 m and the two complete one round in 12 seconds and 16 seconds respectively. After what time (in seconds) from the start will the faster person meet the slower person for the last time?

A) 132     B) 120     C) 138     D) 144        E) None

Explanation: Ashwini and Alpana complete one round in 12 seconds and 16 seconds respectively.

∴ Speeds of Ashwini and Alpana are

960 /12 and 960 /16 i.e. 80 m/s and 60 m/s respectively.

Relative speed of Ashwini with respect to

Alpana = (80 − 60) m/s = 20 m/s

Hence, Ashwini meets Alpana after every

960/20 = 48 seconds

To complete 14.4 km, number of rounds

required = 144/ 9.6 = 15

Since Ashwini is faster, she will win therace and therefore race time =15× 12 = 180 seconds

Since both of them meet each other after every 48 seconds, after the start, Ashwini will meet Alpana 3 times during the race. Time when both of them will meet for the last time = 48 × 3 = 144 seconds

Ans: D

3. During normal hours, a motorcyclist can cover a distance of 136 km in 2 hours but during the peak hours due to traffic his speed is decreased by 20%. If the motorcyclist wants to travel 190.4 km during normal hours and return the same distance during peak hours, then total how much time will he take to cover the journey?

A) 6 hrs 18 min        B) 6 hrs 24 min         C) 6 hrs 30 min           D) 6 hrs 36 min        E) None of these

Explanation: During normal hours, the speed of motorcyclist

=136/2 = 68 km per hour

During peak hours, his speed = 80% of 68

= 54.4 km per hour

The total time taken by him to travel 190.4 km during normal hour = 190.4/68

= 2.8 hours

The total time taken by him in the journey

= (3.5 + 2.8 ) = 6.3 hours

= 6 hrs 18 min

Ans: A

4. Lewis and John run a 10 km race on a circular track of length 1000 m. They complete one round in 200 seconds and 400 seconds respectively. After how much time from the start will the faster person meet the slower person for the last time?

A) 500 seconds     B) 1000 seconds      C) 2500 seconds          D) 1500 seconds         E) 2000 seconds

Explanation: Let us say Lewis meets John after ‘t’ seconds he starts from the starting point.Speeds of Lewis and John are 5 m/s and

2.5 m/s.

t = 1000 / 5 − 2.5 = 400 seconds

Distance travelled by Lewis when meets John for the first time = 2000 m i.e., after 2 complete revolutions. Lewis can make 10 complete revolutions. As he meets John after every two revolutions he would meet John after the 10 th revolution for the last time i.e.,after 400× 5 = 2000 seconds.

Ans: E

5. Arun has to meet Anita at a restaurant at 2:30 PM. He starts from his home when his wrist watch shows 12:30 PM and he knows he should have left 30 minutes before to reach on time, so he speeds up and reaches the restaurant when his wrist watch shows 2:30 PM. When he talks to Anita after reaching the restaurant he comes to know that he has actually arrived 30 minutes early and also that his watch is running 30 minutes ahead of time. To complete the journey on time by how much percent he had to increase his average speed?

A) 20%          B) 33.33%          C) 25%        D) 66.66%         E) None of these

Explanation: At home                       At restaurant

Actual time: 12:00 --------- 2:00 ----- 2:30

Wrist watch time: 12:30 ------------ 2:30

As per wrist watch Arun leaves home at 12:30 PM and arrives at restaurant at 2:30 PM. Wrist watch is 30 minutes ahead so he leaves at 12:00 noon and arrives at 2:00 PM

Journey time (T') = 2 hrs

Actual journey time (T) = 2 hrs 30 min

Time is inversely proportional to speed 30 min time is inversely proportional to speed

Ans: C

6. A bus is 460 m in front of the boy. The boy starts running towards the bus and at the same time the bus starts moving away from the boy. If the speed of the bus is 3m/s and the speed of the boy is 20 km/hr. In how much time will the boy catch the bus?

A) 60 seconds          B) 90 seconds       C) 180 seconds           D) 120 seconds           E) 150 seconds

Explanation: Let the boy catch the bus after ‘t’ seconds.

Speed of the boy = 20 km/hr

Speed of the bus = 3 m/s

The time taken by the boy to catch the bus =460/50/9-3 = 460/9/50-27 = 180 seconds

Ans: C

7. A and B are running on the boundary on two concentric circles with radii in the ratio 2 : 3. The speed ratio of A and B is 8 : 9, where A is running on the inner and B is running on the outer circle. Their starting points form a right angle at the centre of the circle. They both start running in same direction and after 7 seconds B completes a quarter of the outer circle. After how much time the distance between A and B will be minimum?

A) 35 sec          B) 49 sec             C) 56 sec           D) 63 sec             E) None of these

Explanation:

Speed of A and B = S1 and S2

If Q is the angle covered then the distance Covered on circle of radius R = Q × R

Speed of A and B will be proportional to the distance covered by them. Ratio of the distance covered on circle

Previously angle between them was 90° and then 120°, change = 30° in 7 seconds. Distance between A and B will be the minimum when their positions are collinear with the centre.

Initially, angle difference between their positions = 270°

Angle change in 7sec = 30°

( A advances towards B by 30°) 270° change in 7 × 9 = 63 seconds

Ans: D

8. A person wants to travel to Indore which is 360 km from Bhopal. He travels half of the distance by bus then had lunch for 20 minutes in a dhaba. He then took a taxi to cover one-fourth of the distance and then took lift on a motorcycle to cover the distance left. The speed of bus, taxi and motorcycle is 90 km/hr, 60 km/hr and x km/hr respectively. If the bus starts at 9 AM then by what range the value of x varies so that he reaches his destination after 2 PM.

A) 90 ³ x ³ 80         B) 60 ³ x ³ 45            C) 120³ x ³ 90              D) 80³ x ³ 70            E) None of these

Explanation: Bhopal ..... 360 km ..... Indore Distance covered by the bus = 180 km. Speed of the time taken by the bus to cover 180 km

= 180 / 90 = 2 hours

Time for lunch = 20 mins

Distance covered by taxi = 360 / 4 = 90 km

Speed of taxi = 60 km/hr

Time taken by the taxi to cover 90 km

= 90× 60 /60 = 90 mins.

Time he took till now = 2 + 20 mins + 90 mins

= 3 hrs 50 min

Exact time at this point = 12:50 PM

Now, distance covered by the motorcycle = 360 − 180 − 90 = 90 km

Speed of the motorcycle = x km/hr

Let’s take the values from options,

x = 90 km/hr, time taken = 90 / 90  = 1 hour

time = 12:50 + 1 hour = 1:50 PM

x = 80 km/hr, time taken =90 x 60/.80

= 67. 5 min

time =12:50 + 67.5 mins = 1:57 PM

90× 60

x = 60 km/hr, time taken = 90 x 60 / 60

= 90 min

time = 12:50 + 90 mins = 2:20 PM

x = 45 km/hr, time taken = 90× 60 / 45

= 120 min

time = 2:50 PM

x =120 km/hr, time taken =    90× 60 / 120

= 45 min

time = 1 : 35 pm

It can be seen that for the values 60 x 45, he reaches Indore after 2 PM

Ans: B

Posted Date : 27-07-2023

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