APTITUDE TEST 1

Example Quiz 1

1. If a number when divided by 296 gives a remainder 75, find the remainder when 37 divides the same number.

                (A) 36                   (B) 37
                 (C) 38                   (D) 39

2. It takes 20 seconds for a train running at 54 k mph
to cross a platform.And it takes 12 second for the same train in the same speed to cross a man walking at the rate of 6 k mph in the same direction in which the train is running. What is the length of the train and length of platform (in meters).

                 (A) 110, 120           (B) 160, 120
                  (C) 150, 110           (D) 160, 140

3. A and B can complete a work in 12 days.B and C can complete the same work in 18 days. C and A can complete in 24 days. How many days will take for A, B and C combined together to complete the same amount of work?

                 (A) 8(1/13) days       (B) 9(1/13) days
                 (C) 10(1/13) days     (D) 11(1/13) days

4. A person covers a certain distance at a certain speed. If he increases his speed by 33 1/3%, he takes 15 minutes less to cover the same distance. Find the time taken by him initially to cover the distance at the original speed.

                (A) 1 hour             (B) 1.5 hours
                 (C) 2 hours            (D) 2.5 hours

5. The age of a man is three times the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man.

            (A) 44 yrs                (B) 45 yrs
             (C) 46 yrs                (D) 47 yrs

6. Find the average of first 20 natural numbers which are divisible by 7.

            (A) 70.5                     (B) 71.5
             (C) 72.5                     (D) 73.5

7. A man can row 18kmph in still water. It takes him thrice as long as to row up as to row down the river. Find the rate of stream (in kmph).

             (A) 6                          (B) 7
              (C) 8                          (D) 9

8. The average age of three boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is

             (A) 21                          (B) 18
              (C) 15                          (D) 19

9. What is the ratio in which the two types of wheat mixed where the price of the first type is $9.30 per kg and the second type is $10.80 per kg so the mixture is having worth $10 per kg?

           (A) 7:8                          (B) 8:7
            (C) 6:7                          (D) 7:6

10. The production of rice increased by 50% from 1995 to 1996.By what percentage should the production of rice be increased from 1996 to 1997, so that the production of rice in 1997 becomes six times that of 1995?

         (A) 300%                  (B) 400%
          (C) 350%                  (D) 250%




Detailed Answer Key

Question no.1

Question no.2

Question no.3

Question no.4

Question no.5

Question no.6

Question no.7

Question no.8

Question no.9

Question no.10
jQuery UI Accordion - Default functionality
Let the number be ‘x’

Then x = 296k + 75, where ‘k’ is quotient when ‘x’ is divided by ‘296’

In the above sentence we have 296 is multiplied by the constant "k", 75 is added to that. In this form , we consider the number 75 as remainder when the number x is divided by 296.

We want to find the remainder when we divide the number "x" by 37. To do this, we need to have 37 at the place where we have 296 in the above equation.

So we can write 296 as 37 times 8 and 75 as 37 times 2 plus 1. It has shown below.

x = 37 × 8k + 37 × 2 + 1
x = 37(8k + 2) + 1

When the number ‘x’ is divided by 37,the remainder is ‘1’


jQuery UI Accordion - Default functionality
Let "x" and "y" be the lengths of the train and platform respectively

Relative speed of the train to man = 54-6 = 48 kmph
= 48X5/18 m/sec = 40/3 m/sec

When train passes the man, it covers its own length in the above relative speed, length of the train = Relative Speed X Time
= (40/3)X12 = 160 m

And,speed of the train = 54 kmph = 54X5/18 m/sec = 15 m/sec
The train takes 20 seconds to cross the platform.
That is, the train takes 20 seconds to cover (x+y) m distance

Distance /Speed = Time

(x+y)/15=20--->160+y = 300---> y = 140 m

Hence the lengths of the train and platform are 160 m and
140 m respectively


jQuery UI Accordion - Default functionality
From the given information, we can have

(A+B) can complete(1/12) part of the work in 1 day
(B+C) can complete (1/18) part of the work in 1 day
(A+C) can complete (1/24) part of the work in 1 day

By adding the three equations, we get,

(A+B)+(B+C)+(A+C)= 1/12+1/18+1/24
2A+2B+2C=(6+4+3)/72
2(A+B+C)=13/72
(A+B+C) can complete 13/144 part of the work in 1 day

Therefore (A+B+C) can together complete the work in 144/13 days

That is 11(1/13) days


jQuery UI Accordion - Default functionality
If the original speed is 100%,
speed after increment is 133 1/3%.

Ratio of the speeds is 100%: 133 1/3%-->100%:(400/3)%
So, ratio of the speeds is 1:4/3

If the ratio of the speed is 1:4/3, ratio of time taken would be 1:3/4

When the speed is increased by 33 1/3%, 3/4 of the original time is enough to cover the same distance.
That is,when the speed is increased by 33 1/3%, 1/4 of the original time will be decreased.
The question says that when speed is increased by 33 1/3%, time is decreased by 15 minutes.

Therefore, 1/4 of the original time = 15 minutes
Original time = 4X15 = 60 minutes

Hence, time taken by him initially = 60 mins or 1 hour


jQuery UI Accordion - Default functionality
Let "x" be the present age of the man and "y" be the sum of the present ages of two sons.

The present age of the man is three times the sum of the ages of two sons
x = 3y ------(1)

5 years hence, age of the man will be double the sum of the ages of his two sons
x+5 = 2(y+5+5)
x+5 = 2(y+10)
3y+5 = 2y+20........using equation(1)
Solving the above equation, we get y = 15

Plugging y=15 in equation(1),
x = 3(15)
x = 45 yrs

Hence the present age of the man is 45 years.


jQuery UI Accordion - Default functionality
Clearly, the first natural number which is divisible by 7 is 7. The next numbers which are divisible by 7 are 14, 21.....

Let us write the first twenty natural numbers which are divisible by 7. They are 7,14,21,28........ up to 20 terms.

Sum of all the above numbers
= 7+14+21+28.........up t0 20 term

Since all of the above numbers are divisible by 7, we can factor 7
= 7(1+2+3+4+.........+20)
Therefore, sum = 7(210)

Average = (sum of all 20 numbers)/20
Average = (7X210)/20 = 73.5

Hence, the average of first 20 natural numbers which are divisible by 7 is 73.5


jQuery UI Accordion - Default functionality
Let "x" be the speed upstream.
Then the speed downstream = 3x

Rate in still water = 1/2(3x+x)= 2xkm/hr
Therefore 2x = 18 ===> x = 9

Speed upstream = 9 km/hr
Speed downstream = 3X9 = 27 km/hr

rate of the stream = 1/2(27-9) = 9 km/hr


jQuery UI Accordion - Default functionality
From the given ratio, ages of the three boys are 3x, 5x and 7x.

Average of the ages = 5x

Average of the ages = 25 (given)

Then we have 5x=25 ===> x=5

Hence, the age of the youngest boy = 3x5 = 15 years.


jQuery UI Accordion - Default functionality
From the given information, we have

cost price of the cheaper (c) = $9.30
cost price of the dearer (d) = $10.80
cost price of the mixture (m) = $10

Rule to find the ratio for producing mixture is (d-m):(m-c)
(d-m):(m-c) = (10.8-10):(10-9.3) = 0.8:0.7 =8:7

Hence the ratio in which the first kind and second kind to be mixed is 8:7


jQuery UI Accordion - Default functionality
Let 100 tons be the production of rice in 1995

1995 ===> 100 tons
1995-1996 ===> 150 toms (because production has been increased by 50%)
1996-1997 ===> 600 tons (six times production in 1995)

When we look in to the above calculations, it is very clear that the production of rice has been increased 450 tons in 1996 - 97 from 150 tons in 1996.

Percentage of increase in 1996-1997 = (450/150)X100%
= 3X100%=300%

Hence percentage of rice production increased from 1996 to 1997 is 300%

Apart from the stuff given above,  if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

RSS

  1. De Moivre's Theorem and Its Applications

    Apr 19, 24 08:30 AM

    De Moivre's Theorem and Its Applications

    Read More

  2. First Fundamental Theorem of Calculus - Part 1

    Apr 17, 24 11:27 PM

    First Fundamental Theorem of Calculus - Part 1

    Read More

  3. Polar Form of a Complex Number

    Apr 16, 24 09:28 AM

    polarform1.png
    Polar Form of a Complex Number

    Read More