Q.1.Priyanka running at 10 km/hr in a 200 m race giving Ritu a start of 32 metres, beats her by 12 seconds. At what speed Ritu is running?

a) 7.2 km/hr

b) 3.6 km/hr

c) 15 km/hr

d) 18 km/hr

Sol : Option A Explanation: Time taken by Priyanka = 200/10x18/5 = 72 seconds. Distance covered by Ritu = (200 – 32) = 168 m. Time taken by Ritu to cover that distance = (72 + 12) = 84 seconds. Speed of Ritu = 168/84x18/5 = 7.2 km/hr

Q.2. >In a game of billiards, Aman can give Baman 14 points in 70 and Baman can give Chaman 10 points in 80. How many can Aman give Chaman in a game of 100?

a) 12 points

b) 18 points

c) 30 points

d) 28 points

Sol : Option C Explanation:When Aman scores 70 points, Baman scores (70 – 14) = 56 points
⇒ Aman : Baman = 70:56 = 5:4
Also, when Baman scores 80 points, Chaman scores (80 – 10) = 70 points
⇒ Baman : Chaman = 80:70 = 8:7
⇒ Aman : Baman : Chaman = 10:8:7
⇒ when Aman scores 100 points, Chaman scores 70 points
⇒ Aman can give Chaman (100 – 70) = 30 points

Q.3. Three runners Azad, Baghi and Milkha runs a race, with the runner Azad finishing 20 metres ahead of runner Baghi and 28 metres ahead of runner Milkha, while runner Baghi finishes metres ahead of runner Milkha. Each runner travels the entire distance at a constant speed. What was the length of the race?

a) 48 m

b) 36 m

c) 60 m

d) 72 m

Sol : Option B Explanation:: Let the length of the race = x metres
When Azad finishes x m, Baghi covers (x – 20) m and Milkha covers (x – 28) m
⇒ Speed of Baghi : Speed of Milkha = (x – 20):(x – 28)
Also, when Baghi finishes x m, Milkha covers (x – 18) m
⇒ Speed of Baghi : Speed of Milkha = x : (x – 18)
⇒ x-20/x-28 = x/x-18 ⇒ x^{2} – 38x + 360 = x^{2} – 28x ⇒ x = 36

Q.4.

A swimming pool is of 100 m. P and Q enter a 400 m race starting simultaneously at one end of the poll at speeds of 4 m/s and 5 m/s. How many times will they meet while travelling in opposite directions before Q completes the race?

a) two

b) three

d) five

d) seven

Sol : Option B Explanation: Let X be the starting point and Y be the other end point
Time taken by Q to complete 1st lap = 100/5 = 20 sec and time taken by Q to complete the whole race = 400/5 = 80 sec. Likewise, time taken by P to complete 1st lap = 100/4 = 25 sec and time taken by P to complete the whole race = 400/4 = 100 sec

P

Q

Time (sec)

Position

Time (sec)

Position

0

X

0

X

25

Y

20

Y

50

X

40

X

75

Y

60

Y

100

Y

80

Y

Time

P

Q

Opposite

0 to 20

X to Y

X to Y

20 to 25

X to Y

Y to X

✔

25 to 40

Y to X

Y to X

40 to 50

Y to X

X to Y

✔

50 to 60

X to Y

X to Y

60 to 75

X to Y

Y to X

✔

75 to 80

Y to X

Y to X

Q.5.Amar and Prem run a 100 metre race, where Amar beats Prem by 10 metres. To do a favour to Prem, Amar starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

a) Amar and Prem reach the finishing line simultaneously

b) Prem beats Amar by 1 metre

c) Prem beats Amar by 11 metres

d) Amar beats Prem by 1 metre

Sol : Option D Explanation:In a 100 m race, when Karan covers 100 metres, Arjun covers (100 – 10) = 90 metres.
⇒ Speed of Karan : Speed of Arjun = 100:90 = 10:9
In second 100 m race, now Karan has to cover 110 metres to finish the race.
Since speeds are constant, when Karan will cover a distance of 110 m (10 × 11), Arjun covers a distance of 9 × 11 = 99 m
⇒ Karan still beats Arjun by (100 – 99) = 1 metre.

Q.6.P can run one full round of a circular track in 15 min and Q in 35 min. If both P and Q start simultaneously from the same starting point, then how many times would they meet in the time Q has completed 12 rounds when running in same direction and opposite direction respectively?

a) 12, 28

b) 16, 40

c) 40, 16

d) 15, 35

Sol : Option B Explanation:Time ratio to complete one round, P:Q = 15:35 = 3:7 ⇒ Speed ratio P:Q = 7:3
⇒ when Q has completed 12 rounds, P must have completed 12 × 7/3 = 28
While running in same direction, P would have run (28 – 12) = 16 rounds more than Q and would have met 16 times and while running in opposite direction, P would have run (28 + 12) = 40 rounds more than Q and would have met 40 times.

Q.7.Raghu and Rajan runs at 4 km on a course of 250 m round. If their constant speeds be 5:4, how often does the winner passes the other?

a) Raghu passes Rajan thrice

b) Raghu passes Rajan twice

c) Raghu passes Rajan once

d) Rajan passes Raghu twice

Sol : Option A Explanation:Let the speed of Raghu = 5x m/s and Rajan = 4x m/s
Time taken by Raghu to pass Rajan for the 1st time = 250/5x-4x = 250/x sec
Time taken by Raghu to finish the race = 400/5x = 800/x sec
Number of times Raghu passes Rajan = (800/x)/(250/x) = 3.2 ⇒ 3 times

Q8.In a 4000 metre race around a circular stadium having a circumference of 1000 metres, the fastest runner and the slower runner reach the same point at the end of the 5th minute, for the first time after the start of the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

a) 20 min

b) 15 min

c) 10 min

d) 5 min

Sol : Option C Explanation:Let speed of slower runner = x m/min ⇒ Speed of faster runner = 2x m/min Time taken to meet for the 1st time = 1000/2x-x = 5 min ⇒ x = 200 m/min ⇒ 2x = 400 m/min Time taken by the faster runner to finish the race = 4000/400 = 10 min

Q9.A and B start running along a circular track from the same point at the same time in the same direction. To cover the whole track A needs 5 seconds less than B. They meet for the first time after 30 seconds. How many times will they meet in a minute if they run in opposite directions?

a) 18

b) 3

c) 7

d) 6

Sol : Option C Explanation:Let speed of slower runner = x m/min ⇒ Speed of faster runner = 2x m/min Time taken to meet for the 1st time = 1000/2x-x = 5 min ⇒ x = 200 m/min ⇒ 2x = 400 m/min Time taken by the faster runner to finish the race = 4000/400 = 10 min

Q10.Sachin, Saurav and Sehwag started running on a circular track of length 2400 m at the same time from the same point with constant speeds 45 km/hr, 15 km/hr and 35 km/hr respectively. While, Sachin and Sehwag are running in same direction, Saurav is running in the opposite direction. How many complete rounds have Sehwag covered while they meet for the 1st time?

a) 4

b) 3

c) 7

d) 6

Sol : Option B Explanation:Time taken by Sachin and Saurav to meet for the 1st time = 2.4/45+15 = 0.04 hrs Time taken by Sachin and Sehwag to meet for the 1st time = 2.4/45-35 = 0.24 hrs LCM (0.04, 0.24) = 0.24 hrs Distance covered by Sehwag = 35 × 0.24 = 8.4 km Number of complete rounds covered by Sehwag = 8.4/2.4 = 3.5 ≈ 3 (complete rounds)