Quant Quiz

(1) The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

1.   58

2.   48

3.   30

4.   20

(2) The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

1.   17 : 18

2.   8 : 9

3.   Cannot be determined

4.   21 : 22

(3)  A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is

1. 4:5

2. 9:5

3. 8:5

4. 9:2

(4) How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

1. 36 kg

2. 42 kg

3. 54 kg

4. 63 kg

(5) 8 litres are drawn from a cask full of wine and is then filled with water.This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

1. 18 litres

2. 24 litres

3. 32 litres

4. 42 litres

(6)  The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

1.     Rs. 2000

2. Rs. 2200

3. Rs. 2400

4. Data inadequate

(7)  Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
1. 10
2. 15
3. 12
4. 20

(8)  In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

1. 67 kg.

2. 68 kg.

3. 69 kg.

4. Data inadequate

(9)  A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?

1. 26 minutes and 18 seconds

2. 42 minutes and 36 seconds

3. 45 minutes

4. 46 minutes and 12 seconds

(10)  There is 60% increase in an amount in 6 years at simple interest. What will be the compound  interest of Rs. 12,000 after 3 years at the same rate?

1. Rs. 2160

2. Rs. 3120

3. Rs. 3972

4. Rs. 6240


ANSWERS WITH SOLUTIONS:
(1)  3
(2) 4
(3) 2    dog : hare = 3*3 leaps of hare :5*1
          9:5

(4) 4

(5) Let the quantity of the wine in the cask originally be x litres.
  Then, quantity of wine left in cask after 4 operations = [x(1-8/X)4]litres
= [x(1-8/X)4] = 16/81
x = 24

(6) 1

(7) Speed of the first train = 120/10 = 12 m/sec.

Speed of the second train =120/15= 8 m/sec.

Relative speed = (12 + 8) = 20 m/sec.

Therefore Required time =(120 + 120)/20  = 12 sec.

(8) 1 Let Arun's weight by X kg.
According to Arun, 65 < X < 72
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required average = 66 + 67 + 68/3            = 201/3                = 67 kg.

(9) 4
L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.

(10) 3