vector india entrance exam solution 2021: APTITUDE

Vector India Entrance Exam 2021 Aptitude Solutions

APTITUDE:

Q. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

1. 120   
2. 240 m         
3. 300 m       
4. none of these

Ans-> b) 240

Q. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

1. 3 km/hr     
2. 5 km/hr       
3. 8 km/hr       
4. 9 km/hr

Ans-> c) 8km/hr

Solution:- Downstream speed=11km/hr(x+y)
Upstream speed =5km/hr(x-y)
                        x+y=11
                        x-y= 5
               – – – – – – – – –
                       2x=16
so x=8

Q. If x=y=2z and xyz=256 then what is the value of x?.

1. 12       
2. 4         
3. 16         
4. 8

Ans-> d) 8

so,  x=y=2z
       xyz=256
      (2z).(2z).(z)=256
     4z^3=256
     z^3=256/4 =64
     z^3=4^3
     z=4  ,hence,x=2z
  ans =2*4=8

Q. Pipe A can fill a tank in 20 minutes and Pipe B in 30 mins and Pipe C can empty the same in 40 mins.If all of them work together, find the time taken to fill the tank.

1. 17 *1/7 mins     
2. 20 mins         
3. 8 mins         
4. none of these

Solution:-pipe A fill a Tank =1/20
                pipe B  fill a tank=1/30
                pipe C can empty the tank =1/40
               1/20+1/30+-1/40=6+4-3/120
               =7/120
             The tank will fill in 120/7=17*1/7 hours

Q. There is an element which triplicates in every hour. Each of these 3 items in turn reproduce exactly 3 other items. If a single compound is kept in a container at noon and the container is full by midnight. At what time is  container 1/3 full.

1. 4pm       
2. 6pm       
3. 9pm       
4. 11pm

Ans-> a) 4pm

Q. Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?

a) 18 steps       

b) 25 steps       

c) 46 steps         

d) 32 steps

Ans-> b) 25 steps  

Q. What is the missing number in this series? 8 2 14 6 11 ? 14 6 18 12.

1. 7         
2. 5       
3. 9       
4. 10

Ans: 9  

Q. Can you find out what day of the week was January 12, 1979?

1.  Friday       
2. Saturday       
3. monday       
4. Wednesday

Ans-> Friday 

Q. A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?

1.  Rs.17.40 per kg.     
2. Rs. 24.35 per kg.       
3.  Rs. 12.46 per kg       
4. Rs. 22.15 per kg

Q. A garrison of 3300 men has provisions for 32 days, when given at a rate of 850 grams per head. At the end of 7 days a reinforcement arrives and it was found that now the provisions will last 8 days less, when given at the            rate of 825 grams per head. How, many more men can it feed?

1. 1540 men         
2. 1250 men       
3. 1700 men     
4. 250 men

Ans-> c) 1700 men

Q. The sum of a number and the number preceding it is 33. By how much is two less than six times the number?

1. 196             
2. 94             
3. 90           
4. 100

Ans-> d) 100

Q. If the length and breadth of a room are increased by y feet each, the perimeter increases by 16 feet. Find y

1.  8         
2. 2         
3. 6             
4. 4

Ans-> d) 4

Q. One-fourth of a number is greater than one-fifth of the number succeeding it by 1. Find the number.

1. 24       
2. 42       
3. 36         
4. 48

Ans-> c) 36

Q. An oil cylinder was 3/4th full. When two bottles of oil is poured into it, it is 4/5th full. How many bottles of oil can the full cylinder hold?

1. 20     
2. 15       
3. 40       
4. 30

Ans-> c) 40

Solution:-4/5-3/4=2bottles
                1/20=2bottles
                20/20=40bottles

Q. The ratio of present age of A and B is 4:3. A will be 26yrs old in 6yrs from now. How old is B now?

1. 15yrs       
2. 20yrs       
3. 25yrs       
4. 0yrs

Ans-> a) 15yrs

Q. A profit of Rs. 500 is divided between X and Y in the ratio of ½ : 1/3 .What is the difference between their profit shares ?

1. Rs. 200     
2. Rs. 100     
3. Rs. 300     
4. Rs. 50

Ans-> b) Rs. 100

67. The sum of the present ages of A, B, C is 45 yrs. Three years ago their ages were in the ratio 1:2:3. What is the present age of A

1. 10yrs       
2. 6yrs         
3. 8yrs               
4. 9yrs

Ans-> c) 8yrs

Q. If the denominator of a fraction is increased by 4, then the fraction becomes 5/8. If the numerator is 11 less than the denominator, find the numerator.

1.  25     
2.  20     
3.  30       
4. 35

Ans-> a) 25

Q. 15-mangoes and 7-apples cost as much as 10-mangoes and 9-apples. What is the ratio of cost of one mango to cost of one apple?

1. 2:5     
2. 5:2     
3. 3:4       
4. Cannot be determined

Ans-> 2:5    

Q. A person sold his watch for 96 $ and got some percentage of profit which was numerically equal to the cost price. What is the cost price of the watch

1. 50 $     
2. 54 $     
3. 60 $       
4. 80 $

Ans-> c) 60 $ 

Q.  Tap A can fill an empty tank in 6-hours and Tap B can empty the full tank in 8-hours. If the tank is empty when tap A is opened at 9:00 am and tap B is opened at 11:00 am, then at what time is the tank filled?

1. 6:00pm     
2. 3:00 am     
3. 3:00pm         
4. 6:00am

Ans-> b) 3:00 am   

Q. 20 men can plant 50 saplings in 8-hours. In how many hours can 15men plant 80 saplings?

1. 17 1/25         
2. 12 7/11       
3. 20         
4. None of these

Q. A man can row at 6 km/h in still water and at 4 km/h upstream. How long will the man take to go to a place 1 km downstream and return?

1. 36 min         
2. 24 min       
3. 12 min         
4. 18min

Ans-> b) 24 min      

Q. Some telegraph poles are placed 20 m apart. How many poles will a train pass in 3- hours at 60km/h ?

1. 1200         
2. 2500         
3. 4000           
4. 9000

Ans-> d) 9000

Q. The square of a two digit number is divided by half the number. After 36 is added to thequotient, this sum is then divided by 2. The digits of the resulting number are the same as those in the original number, but they are in            reverse order. The ten's place of the original number is equal to twice the difference between its digits. What is the number?

1. 38         
2. 46         
3. 27         
4. 75