Quantitative Aptitude Quiz Set-09
1. A train with 90 km/h crosses a bridge in 36 seconds. Another train 100 metres shorter crosses the same bridge at 45 km/h. What is the time taken by the second train to cross the bridge ?
A.61 seconds
B.63 seconds
C.62 seconds
D.64 seconds
2. Ramesh travels 760 km to his home, partly by train and partly by car He takes 8 hours, if he travels 160 km by train and the rest by car. He takes 12 minutes more, if he travels 240 km by train and the rest by car. What are the speeds of the train and of the car?
A.Speed of car = 90 km/h, speed of train = 60 km/h
B.Speed of car = 100 km/h, speed of train = 80 km/h
C.Speed of car = 80 km/h, speed of train = 70 km/h
D.Speed of car = 100 km/h, speed of train = 90 km/h
3. The average score of boys in an examination in a school is 71 and that of the girls is 73. The average score of the school is 71.8. The ratio of the number of boys to that of the girls that appeared in the examination is
A.1 : 2
B.3 : 2
C.2 : 2
D.4 : 2
4. Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak’s share is :
A. Rs. 540
B. Rs.7200
C. Rs. 8400
D. Rs. 9600
5. A, B and C enter into a partnership and theirs shares are in the ratio 1/2 : 1/3 : 1/4. After two months, A withdraws half of his capital and after 10 months, a profit of Rs.378 is divided among them. What is B’s share?
A. Rs.129
B. Rs.144
C. Rs.156
D. Rs.168
6. The head of a fish is 6 inches long. Its tail is as long as its head and half its body. If its body is half of its whole length, how long is the fish?
A.16 inches
B. 24 inches
C. 32 inches
D. 48 inches
7. There are 3 cars moving at speeds in the ratio of . If the fastest car covers 10 km more than the car with medium speed in 30 minutes, then the speed of the slowest car in kmph is:
A. 30 kmph
B. 60 kmph
C. 75 kmph
D. 100 kmph
8. Kiran received Rs. 6000 as his share out of the total profit of Rs.9000 which he and Arun earned at the end of one year. If Kiran invested Rs. 30,000 for 6 months, whereas Arun invested his amount for the whole year, what was the amount invested by Arun?
A. Rs.5000
B. Rs.6000
C. Rs.7000
D. Rs.7500
Answers
Answer 1: Option D.
Explanation:
Train A, Speed = 90kmph
=90*(5/18)m/s = 25m/s = 25m/s, t=36s
Let length, L = x+y = time*speed = 25*36 = 900m
=800m, Speed= 45*(5/18) = (25/2) m/s
t= (Distance/Speed) = (800/(25/2)) = (1600/25) = 64 seconds
Answer 2: Option B.
Explanation:
Let speeds be x and y for train and car respectively.
Then 8 = (160/8) + (600/y) …..(1)
And 8(1/5) = (240/x) + ((760-240)/y) …..(2)
Solving for x and y, we get 100 and 80 km/hr.
Answer 3: Option D.
Explanation:
71.8 = (71x+73y)/(x+y)
71.8 (x+ y) = 71x + 73y
0.8x = 1.2y
x:y = 12:8 which is equals to 3:2
Answer 4: Option C.
Explanation:
Ratio of their shares = 22500 : 35000 = 9 : 14.
Deepak’s share = Rs. 13800 * 14/23
= Rs. 8400
Answer 5: Option B.
Explanation:
Exp: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
Therefore, B’s share = Rs. 378 * 8/21
= Rs.144.
Answer 6: Option D
Explanation:
Given, tail T = H+B/2 , where H is the head and B is the body.
Also, B = L/2 , where L is the whole length.
Here, whole length L= H+B+T
Answer 7: Option B
Explanation:
Let the speeds of the three cars be 1.5y kmph, 2.5y kmph, and 3y kmph.
The fastest car, then, covers 3y/2 km in 30 minutes.
Therefore, the speed of the slowest car is (1.5 × 40) = 60 kmph.
Answer 8 :
Explanation:
Suppose Arun invested Rs.x. Then, Kiran : Arun = (30000 * 6) : (x * 12)
Therefore, 180000 = 6000 or x = 18000 = 7500.
12×3000 24