Numerical Ability Test

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Numerical Ability Test - 5

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Weekly Quiz Competition

Question 1
5 / -1

A motor cyclist completes a certain journey in 5 hours. He covers one-third distance at 60 km/hour and the rest at 80 km/hour. The length of the journey is :

A
180 km

B
240 km

C
300 km

D
360 km

Solution

Given:
Time taken by the motorcyclist = 5 hours
Speed while covering 1/3rd of the distance = 60 km/h
Speed while covering 2/3rd of the distance = 80 km/h
Formula used:
Time = Distance/Speed
Calculation:
Let the length of the entire journey = 3a
As per the question;
(3a × 1/3)/60 + (3a × 2/3)/80 = 5
⇒ a/60 + 2a/80 = 5
⇒ (4a + 6a)/240 = 5
⇒ 10a/240 = 5
⇒ a = 120
⇒ 3a = 3 × 120 = 360
∴ The entire journey is of 360 km.
Question 2
5 / -1

A train covers 40 km in 45 minutes and next 60 km in 80 minutes. What is its average speed for whole journey in km/h?

A
48

B
54

C
50

D
60

Solution

Given:
40 km travelled in 45 minutes and next 60 km travelled in 80 minutes
Formula used:
Average speed = total distance/total time
Calculation:
Total time = 45 + 80 = 125 min = 125/60 hours
Average speed = (40 + 60)/(125/60) = 1200/25
∴ Average speed for the whole journey = 48 kmph
Question 3
5 / -1

A 100 m long train is running at a speed of 70 km/h. In what time will it pass a man who is running at 10 km/h in the same direction in which the train is going?

A
1 sec

B
2 sec

C
3 sec

D
6 sec

Solution

Given:
Length of train = 100 m and Speed = 70 km/h
After pass a man the speed of train = 10 km/h
Formula used:
Speed = Distance/Time
Time = Distance/Speed
Concept used:
When they are moving in the same direction, the relative speed between the two bodies is the difference of their speeds,
(u – v) if u > v
(v – u) if v > u.
Calculation:
Speed of train with respect to man = 70 - 10 = 60 km/hr = 60 × 5/18 = 50/3 m/sec
Time taken by it to cover 100m distance at 50/3 m/s speed.
⇒ 100 × 3/50 = 6 sec
∴ The required answer will be 6 sec.
Question 4
5 / -1

If downstream speed of a motorboat is 16 km/h and its upstream speed is 11 km/h. Find the speed of stream in km/h ?

A
2.5 km/h

B
3.5 km/h

C
3 km/h

D
3.8 km/h

Solution

Given:
The downstream speed of a motorboat is 16 km/h
The upstream speed of the motorboat is 11 km/h
Formula:
Speed of current = (Rate of downstream - Rate of upstream)/2
Calculation:
According to the formula,
Speed of current = (16 - 11)/2
⇒ (16 - 11)/2
⇒ 5/2 = 2.5 km/h
∴ The speed of the stream is 2.5 km/h.
Question 5
5 / -1

The train running at the speed of 72 km/h goes past a pole in 15 s. What is the length of the train?

A
150 m

B
200 m

C
300 m

D
350 m

Solution

Formula used:
Distance = Speed × Time
Concept used:
1 km/h = 5/18 m/s
Calculation:
Speed of the train = 72 km/h = 72 × (5/18) = 20 m/s
Length of the train = Speed × time = 20 × 15 = 300 m
∴ The length of the train is 300 m
Question 6
5 / -1

A thief steals a car at 5 PM and drives it at 40 km/h. The theft is known to police is at 5:30 PM and the police sets off in another car at 60 km/h. When will he overtake the thief?

A
6:30

B
4:30

C
3:30

D
6:00

Solution

Concept used:
When they are moving in the same direction, the relative speed between the two bodies is the difference of their speeds,
(u – v) if u > v
(v – u) if v > u.
Calculation:
According to the question,
Distance covered by thief in (5 : 30 - 5) hour = 1/2 × 40 = 20 km
Relative speed of police to thief = 60 - 40 = 20 km/hr
Time taken by police to maintain 20 km = 20/20 = 1 hr.
Then, police will overtake thief at 5 : 30 + 1 : 00 = 6 : 30 PM.
∴ The required answer will be 6 : 30 PM.
Question 7
5 / -1

In a race of 900 meters, Shreya beats Rahul by 15 seconds or 225 meters. Find the time in which Shreya finished the race?

A
30 seconds

B
45 seconds

C
60 seconds

D
40 seconds

Solution

GIVEN:
Length of race = 900 meters
Shreya beats Rahul = 15 seconds or 225 meters.
CONCEPT:
Relative speed.
CALCULATION:
As Rahul lost by 15 seconds or 225 meters, that means he would have covered 225 meters in 15 seconds only.
So, Speed of Rahul = 225/15 = 15 m/s
So,
⇒ Time in which Rahul covers 900 meters = 900/15 = 60 seconds
Hence,
⇒ Time in which Shreya finished the race = 60 – 15 = 45 seconds
Alternate Method
Shreya travels 225 m in 15 seconds
Her speed = 225/15 = 15 m/s
Then, the distance she travels to finish the race = time taken to travel (900 - 225 m)
She finishes the race in = 675/15 = 45 s
∴ The time taken by Shreya to finish the race is 45 seconds.
Question 8
5 / -1

Amit runs 100 m in 25 seconds and Ashok runs 100 m in 20 sec. By what distance will Amit lose the race?

A
10

B
15

C
20

D
25

Solution

GIVEN:
Distance for
Amit = 100m
Ashok = 100m
Time for
Amit = 25 seconds
Ashok = 20 seconds
FORMULA USED:
Speed = Distance/Time
CALCULATION:
Amit’s speed = 100/25 = 4 m/sec
⇒ Ashok’s speed = 100/20 = 5 m/sec
⇒ Distance covered by Ashok in 20 sec = 100 m
⇒ Distance covered by Amit in 20 sec = 4 × 20 = 80 m
∴ Amit lose the race by (100 – 80) m = 20 m
Question 9
5 / -1

A man travelled from a point A to B at the rate of 25 Kmph and walked back at the rate of 4 Kmph. If the whole journey took 5 hrs 48 minutes, the distance between A and B is

A
30 km

B
24 km

C
20 km

D
51.6 km

Solution

Given:
A man goes from point A to B with the speed of 25 km/hr
The man comes from point B to A with the speed of 4 km/hr
Total time to cover whole journey = 5 hrs 48 minutes.
Formula:
Speed = distance/time
1 hr = 60 min
Calculation:
5 hrs 48 min = (5 + 48/60) hr = (5 + 4/5) = 29/5 hr
Let distance between A and B be x km, then
According to the question,
x/25 + x/4 = 29/5
⇒ (4x + 25x)/100 = 29/5
⇒ 29x/100 = 29/5
⇒ x = 29/5 × 100/29
⇒ x = 20
∴ Distance between A and B is 20 km.
Question 10
5 / -1

Two cars start from opposite ends of the road and travel towards each other with speeds of 24 km/h and 30 km/h respectively. The distance between the starting positions of the cars is 86.4 km. The estimated time when both the cars meet each other will be-

A
14.4 Hours

B
2.88 Hours

C
1.6 Hours

D
3.6 Hours

Solution

Given:
Speed of first car = 24 km/h
Speed of second car = 30 km/h
Distance = 86.4 km
Formula used:
When two cars from opposite direction travels towards each other then, Relative speed = (speed of first car + speed of second car)
Speed = Distance/Time
Calculation:
According to the question
Relative speed = (24 + 30) km/h
⇒ 54 km/h
Now,
Time taken to meet both the cars to each other = (86.4/54) hours
⇒ 1.6 hours
∴ The required time is 1.6 Hours

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Numerical Ability Test - 5

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Numerical Ability Test - 5

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SHARING IS CARING

Question 1

180 km

240 km

300 km

360 km

Solution

Question 2

48

54

50

60

Solution

Question 3

1 sec

2 sec

3 sec

6 sec

Solution

Question 4

2.5 km/h

3.5 km/h

3 km/h

3.8 km/h

Solution

Question 5

150 m

200 m

300 m

350 m

Solution

Question 6

6:30

4:30

3:30

6:00

Solution

Question 7

30 seconds

45 seconds

60 seconds

40 seconds

Solution

Question 8

10

15

20

25

Solution

Question 9

30 km

24 km

20 km

51.6 km

Solution

Question 10

14.4 Hours

2.88 Hours

1.6 Hours

3.6 Hours

Solution

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