Quantitative Aptitude

General Questions

Quantitative Aptitude Exercise Mode

General Questions

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Question 21
A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m ?

A
5
B
6
C
7
D
8
Correct Answer: Option A

Relative speed = (2 + 3) = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 7 times before 9.30 a.m.

Question 22
A thief steals a car at 2.30 p.m. and drives it at 60 kmph. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 kmph. When will he overtake the thief ?

A
4.30 p.m.
B
4.45 p.m.
C
5 p.m.
D
5.15 p.m.
Correct Answer: Option C

Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the thief in x hrs
= distance covered by the owner in (x - 1/2) hrs.
∴ 60x = 75 (x - 1/2) <=> 15x = 75/2
<=> x = 5/2 hrs.
So, the thief is overtaken at 5 p.m.

Question 23
The distance between two cities A and B is 330 km. A train starts from A at 8 a.m and travels 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 ?

A
10 a.m.
B
10.30 a.m.
C
11 a.m.
D
11.30 a.m.
Correct Answer: Option C

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
∴ 60x + 75 (x-1) = 330
=> x = 3
So, they meet at (8 + 3 )
i.e. 11 a.m.

Question 24
For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat ?

A
15 : 14
B
16 :15
C
12 :11
D
10 : 9
E
None of these
Correct Answer: Option B

Let distance covered by dog in 1 leap is x and
Distance covered by cat in 1 leap is y

Then, 3x = 4y
∴ x= 4/3y

Now, Ratio of speed of dog and cat = Ratio of distance covered by them in the same time = 4x : 5y
= 16/3y : 5y
= 16 : 15

Question 25
Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is :

A
500 km
B
630 km
C
660 km
D
900 km
Correct Answer: Option D

At the time of meeting, let the distance travelled by the the second train be x km.
Then, distance covered by the first train is (x + 100) km.
∴ x /40 = (x + 100) /50

<=> 50x = 40x + 4000
<=> x = 400.

So distance between P and Q = (x + x + 100) km
= 900 km.

Question 26
Mumbai Express left Delhi for Mumbai at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Mumbai on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two train meets ?

A
120 km
B
360 km
C
480 km
D
500 km
Correct Answer: Option C

Suppose they meet x hours after 14.30 hrs.
Then, 60x = 80 (x - 2)
or x = 8

∴ Required distance = (60 X 8) km = 480 km.

Question 27
Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds ?

A
9 : 20
B
11 : 9
C
11 : 20
D
None of these
Correct Answer: Option B

In the same time, they cover 110 km and 90 km respectively.

∴ Ratio of their speeds = 110 : 90 = 11 : 9

Question 28
In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the distance. The time taken by A to reach the destination is :

A
1 hour
B
1 hour 30 minutes
C
2 hours
D
2 hours 30 minutes
Correct Answer: Option C

Ratio of speed = 3 : 4.
Ratio of times taken = 4 : 3.
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.

Then, 4x - 3x = 30/60 = 1/2

or x = 1/2

∴ Time taken by A = 4x hrs = 4 X hrs = 2 hrs.

Question 29
A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, the distance between his house and school is :

A
5 km
B
5.5 km
C
6 km
D
6.5 km
Correct Answer: Option C

Average speed = [(2 X 3 X 2) / (3 + 2) = 12/5 km/hr.

Distance travelled = (12 /5 X 5) km = 12 km.

∴ Distance between house and school :
     = 12/2 km = 6 km.

Question 30
A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to :

A
3 km / hr
B
4 km / hr
C
5 km / hr
D
7 km / hr
Correct Answer: Option B

Let A's speed = x km / hr.
Then, B's speed = (7 - x) km / hr.
So, 24/x + [2 4 / (7 - x ) ] = 14

<=> 24 (7 - x) + 24x = 14x (7 - x)
<=> 14x2 - 98x + 168 = 0
<=> X2 – 7x + 12 = 0
<=> (x - 3) (x - 4) = 0
<=> x = 3 or x = 4.

Since, A is faster than B, so A's speed = 4 km / hr
and B's speed = 3 km / hr.

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