APTITUDE TEST 2

About "Aptitude Test 2"

Aptitude Test 2 : 

The test given in this section can be taken without any login credentials. At the end of the test, you can check you score as well as detailed answer for each question. 

Example Quiz 1

1. Find the number of prime factors of 610 X 717 X 5527.

                (A) 90                   (B) 91
                 (C) 92                   (D) 93

2. Two trains running at 60 kmph and 48 kmph cross each other in 15 seconds when they run in opposite direction. When they run in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. Find the length of the two trains (in meters).

       (A) 300, 130              (B) 310, 115
        (C) 320, 110              (D) 330, 120

3. A & B can do a work in 15 days, B & C in 30 days and A & C in 18 days. They work together for 9 days and then A left. In how many more days, can B and C finish the remaining work ?

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

4. A man traveled from the village to the post office at the rate of 25 k mph and walked back at the rate of 4 kmph. If the entire journey had taken 5 hours 48 minutes, find the required distance of the post office from the village.

           (A) 20 km             (B) 21km
            (C) 22 km             (D) 23 km

5. The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.

            (A) 35 yrs                (B) 34 yrs
             (C) 33 yrs                (D) 32 yrs

6. The average of four consecutive even numbers is 27. Find the largest of these numbers.

            (A) 28                     (B) 30
             (C) 32                     (D) 34

7. A boat takes 19 hours for traveling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?

         (A) 150 km                 (B) 160 km
          (C) 170 km                 (D) 180 km

8. John weighs 56.7 kilograms. If he is going to reduce his weight in the ratio 7:6, find his new weight.

         (A) 48.6 kg                (B) 49.6 kg
          (C) 50.6 kg                (D) 51.6 kg

9. Find the ratio in which, water to be mixed with milk to gain 20% by selling the mixture at cost price.

           (A) 1:5                          (B) 5:1
            (C) 1:7                          (D) 1:7

10. 15% of income of A is equal to 25% of income of B and 10% of income of B is equal to 30% of income of C. If income of C is $ 1600, then total income of A, B and C is

         (A) $ 14200              (B) $ 14300
          (C) $ 14400              (D) $ 14500




Detailed Explanation of Answers

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
From 610 × 717 × 5527, we have to write each base in terms of multiplication of its prime factors.

That is,=(2X3)10×(7)17×(5X11)27

=210X310X717X527X1127

The no. of prime factors = sum of the exponents
= 10+10+17+27+27
= 91

Hence, the number of prime factors is 91.


jQuery UI Accordion - Default functionality
When the two train running in opposite direction, relative speed = 60+48 = 108 kmph = 108X5/18 m/sec = 30 m/sec

Sum of the lengths of the two trains = sum of the distances covered by the two trains in the above relative speed

Sum of the lengths of the two trains = 30X15 = 450 m

When the two trains running in the same direction, relative speed = 60-48 =12 kmph = 12X5/18 = 10/3 m/sec

When the two trains running in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. The distance he covered in 36 seconds in the relative speed is equal to the length of the slower train.

Length of the slower train = 36X10/3 = 120 m

Length of the faster train = 450-120 = 330 m

Hence, the length of the two trains are 330m and 120m


jQuery UI Accordion - Default functionality
We can apply L.C.M method to solve this problem

Total work = 90 units (L.C.M of 15,30,18,9)
(A+B) can complete 6 units/day (90/15 = 6)
(B+C) can complete 3 units/day (90/30 = 3)
(A+C) can complete 5 units/day (90/18 = 5)
By adding, we get 2(A+B+C) = 14 units/day
(A+B+C) = 14/2 = 7 units/day

work done by A = (A+B+C)-(B+C)=7-3=4 units/day
work done by B = (A+B+C)-(A+C)=7-5=2 units/day
work done by C = (A+B+C)-(A+B)=7-6=1 unit/day
work done by (A+B+C)in 9 days = 9X7 = 63 units.
Balance work = 90-63 = 27 units

This 27 units of work to be completed B & C. Because A left after 9 days of work.

No. of days taken by B & C to complete the balance 27 units of work = 27/3 = 9 days. (Because B&C can complete 3 units of work per day)


jQuery UI Accordion - Default functionality
Average speed = 2pq/(p+q), here p=25 q=4
= (2X25X4)/(25+4)
Therefore, average speed = 200/29 km/hr

And 5 hour 48 min = 54860hrs = 29/5 hours
Distance = Speed X Time

Distance = (200/29)X(29/5) = 40 km
Distance covered in 5 hrs 48 min = 40 km

Hence,distance of the post office from the village = 40/2 = 20km


jQuery UI Accordion - Default functionality
Let "x" be the present age of the son.Then the present age of father is (3x+3)

3 years hence, father's age will be 10 years more than twice the age of the son
(3x+3)+3 = 2(x+3)+10
3x+6 = 2x+16
x = 10
To find the present age of the father, plug x = 10 in (3x+3)

Present age of the father = 3(10)+3 = 33 years


jQuery UI Accordion - Default functionality
If "x' be the first even number, then the four consecutive even numbers are x, x+2, x+4, x+6

Average of the four consecutive even numbers = 27

(x+x+2+x+4+x+6)/4 = 27
(4x+12) = 108
4x = 96 ===> x = 24

Hence the largest even number = x+6 = 30


jQuery UI Accordion - Default functionality
From the given information, we have
Speed downstream = (14+4) = 18 kmph
Speed upstream = (14-4) = 10 kmph

Let "x" be the distance between A and B
x/18 + (x/2)/10 =19 (Hint: Time = Distance/Speed)
x/18 + x/20 =19
(10x + 9x)/180 = 19 (L.C.M of 18,20 is 180)
19x/180 = 19
x = 180

Hence the distance between A and B is 180 km.


jQuery UI Accordion - Default functionality
Original weight of John = 56.7 kg (given)

He is going to reduce his weight in the ratio 7:6

[Hint:If a quantity increases or decreases in the ratio a:b, then new quantity = 'b' of the original quantity divided by 'a']

His new weight = (6x56.7)/7 = 6x8.1 = 48.6 kg.


jQuery UI Accordion - Default functionality
Let the cost price of 1 ltr pure milk be $1

Now we take some quantity of milk (less than 1 ltr),add some water and make it to be 1 ltr mixture

Let "x" be the money we invest for milk in 1 ltr of milk-water mixture

Since the gain is 20%, selling price = x + 20%of x
Selling price = 120% of x = (120/100)x = (6/5)x

But the mixture is sold at the cost price of pure milk
So, we have (6/5)x = 1
x = 5/6
Therefore cost price of the milk in the mixture = $(5/6

Cost price of the water = $0

Rule to find the ratio for producing mixture = (d-m):(m-c)
(d-m):(m-c) = 1-5/6:5/6-0 = 1/6:5/6 = 1:5

So, water and milk to be mixed in the ratio to gain 20% is 1:5


jQuery UI Accordion - Default functionality
Let A,B and C be the incomes of A,B and C respectively

From the given information, we have C = $1600
10% of B = 30% of C
(10/100)B = (30/100)X1600
B = $ 4800

15% of A = 25% of B
(15/100)A = (25/100)X4800
A = $8000

A+B+C = 8000+4800+1600 = 14400

Hence, the total income of A,B and C is $14400


After having practiced answering the above questions, we hope that the students would have understood, how to solve quantitative problems  easily.  

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