Quant Quiz

1.A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance(in km) is:
(1)40km                
(2)28                  
(3)42
(4)48                        
(5)none of these

2.A bag contains 6 red and 3 white balls.Four balls are drawn out one by one and not replaced. What  is the probability that they are alternatively of different colours?
(1)4/42    
(2)5/84                            
(3)7/84            
(4)5/42  
(5)none of these

3.What will be the compound interest accrued on an amount of Rs. 10.000 at the rate of 20 p.c.p.a. two years if the interest is compounded half yearly?
(1)Rs.4,400                            
(2)Rs.4,600                    
(3)Rs.4,641
(4)Rs.4,680                            
(5)None of these

4.One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn iS a face card (Jack, Queen and King only)?
(1)1/13      
(2)3/13    
(3)1/4      
(4)9/52    
(5)None of these

5.A monkey tries to ascend a greased pole 14 m high. He ascends 2 m in first  minute and slips 1 min  next alternate minute. If he continues to ascend in this fashion, how long does he take to reach the top?
(1)25                        
(2)24                                  
(3)22
(4)30                          
(5)26

6.Thirty men can do a work in 24 days. In how many days can 20 men do the work , given that timespent  per day is increased by 1/3 of the previous time.
(1)30                    
(2)28                                    
(3)36
(4)27                    
(5none of these

7.The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then value  of x is
(1)15                          
(2)16                                
(3)18
(4)20                          
(5)none of these
         
8.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    
(5)none of these

9.A plane left 30 min later from the schedule time & in order to reach the destination 1500 km on time ,it had increase the speed by 250 kmph from the usual speed,its usual speed is
(1)700kmph                
(2)750kmph                
(3)250kmph
(4)350kmph                  
(5)500kmph

10.A certain distance is covered at a certain speed.if half of this distance is coveredin double the time,the ratio of the two speed is.
(1)4:1                                
(2)1:4                                
(3)1:8
(4)1:6                                
(5)8:1

Answers With Explanation:

1. (1) Let distance be x kmph and speed y kmph
x/y - x/(y+3) = 40/ 60 ............ (i)
x/(y-2) - x/y = 40/60 .............. (ii)
from eqution (i) & (ii)
y = 12 kmph
x = 40 km
2. (4) Red = 6, White = 3
P(E) = RWRW + WRWR
P(E) = 6/9 * 3/8 * 5/7  * 2/6  + 3/9 * 6/8* 2/7 * 5/6
=  5/42
3. (3)
P = 10,000, R = 10 % , T = 4  years
A = P (1 + r/100)^n
= 10000 (1 + 10/100) ^4
= 10000 (11/10)^4   = 14641
C.I = 14641 - 10, 000 = 4641

4. (2)No. of face cord = 4 * 3 = 12
P (E) = 12/52 = 3/13
5(1)
Distance covered in 2 min = 2-1 = 1 meter
2 min = 1
24 min = 12
in next minute ascend = 2 m
25 minute = 14 meter

6(4)  Let no of days required be x
30 * 24 = 20 * x * (1 + 1/3)
x  = 27 days

7 (2)  Since SP of x = CP of 20
SP/CP = 20/x
profit %  = (20 - x)* 100/x
So,(20 -x)100/x  = 25
x = 16

8(1)CP = (1920 + 1280)/2  = 1600
SP = 1600 * 125/100 = 2000

9(2)  Let usual speed be x kmph
1500/x - 1500/(x + 250) = 1/2
By option
x = 750 kmph

10 (1)Let Distance = D
        Time =  T
S1 = D/T
S2 = (D/2)/(2T)
S1/52 = D/T/(D/2)(2T)
S1 : S2 = 4 : 1