# Online Aptitude Test - Aptitude Test 10

Instruction:

• This is a FREE online test. DO NOT pay money to anyone to attend this test.
• Total number of questions : 20.
• Time alloted : 30 minutes.
• Each question carry 1 mark, no negative marks.
• DO NOT refresh the page.
• All the best :-).

1.

The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?

A.
 2010
B.
 2011
C.
 2012
D.
 2013

Explanation:

Suppose commodity X will cost 40 paise more than Y after z years.

Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40

0.25z = 0.40 + 2.10

 z = 2.5 = 250 = 10. 0.25 25

X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.

2.

There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

A.
 20
B.
 80
C.
 100
D.
 200

Explanation:

Let the number of students in rooms A and B be x and y respectively.

Then, x - 10 = y + 10      x - y = 20 .... (i)

and x + 20 = 2(y - 20)      x - 2y = -60 .... (ii)

Solving (i) and (ii) we get: x = 100 , y = 80.

The required answer A = 100.

3.

If a - b = 3 and a2 + b2 = 29, find the value of ab.

A.
 10
B.
 12
C.
 15
D.
 18

Explanation:

2ab = (a2 + b2) - (a - b)2

= 29 - 9 = 20

ab = 10.

4.

The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

A.
 20
B.
 23
C.
 169
D.
 None of these

Explanation:

Let the numbers be x and y.

Then, xy = 120 and x2 + y2 = 289.

(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529

x + y = 529 = 23.

5.

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A.
 3 : 3 : 10
B.
 10 : 11 : 20
C.
 23 : 33 : 60
D.
 Cannot be determined

Explanation:

Let A = 2k, B = 3k and C = 5k.

 A's new salary = 115 of 2k = 115 x 2k = 23k 100 100 10

 B's new salary = 110 of 3k = 110 x 3k = 33k 100 100 10

 C's new salary = 120 of 5k = 120 x 5k = 6k 100 100

 New ratio 23k : 33k : 6k = 23 : 33 : 60 10 10

6.

A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew of his capital and B withdrew of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:

A.
 Rs. 330
B.
 Rs. 360
C.
 Rs. 380
D.
 Rs. 430

Explanation:

 A : B = 4x x 3 + 4x - 1 x 4x x 7 : 5x x 3 + 5x - 1 x 5x x 7 4 5

= (12x + 21x) : (15x + 28x)

= 33x :43x

= 33 : 43.

 A's share = Rs. 760 x 33 = Rs. 330. 76

Direction (for Q.No. 7):

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

7.

 What is R's share of profit in a joit venture? I. Q started business investing Rs. 80,000. II. R joined him after 3 months. III. P joined after 4 months with a capital of Rs. 1,20,000 and got Rs. 6000 as his share profit.

A.
 All I, II and III
B.
 I and III only
C.
 II and III only
D.
 Even with all I, II and III, the answer cannot be arrived at
E.
 None of these

Explanation:

From I, II and III, we get P : Q : R = (120000 x 8) : (80000 x 12) : (x x 9).

Since R's investment is not given, the above ratio cannot be give.

8.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A.
 Rs. 375
B.
 Rs. 400
C.
 Rs. 600
D.
 Rs. 800

Explanation:

 C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 . 3 6 8 3 24 24

 A's wages : B's wages : C's wages = 1 : 1 : 1 = 4 : 3 : 1. 6 8 24

 C's share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400. 24

9.

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

A.
 230 m
B.
 240 m
C.
 260 m
D.
 270 m

Explanation:

 Speed = 72 x 5 m/sec = 20 m/sec. 18

Time = 26 sec.

Let the length of the train be x metres.

 Then, x + 250 = 20 26

x + 250 = 520

x = 270.

10.

If log10 2 = 0.3010, then log2 10 is equal to:

A.
 699 301
B.
 1000 301
C.
 0.301
D.
 0.699

Explanation:

 log2 10 = 1 = 1 = 10000 = 1000 . log10 2 0.301 3010 301

11.

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

A.
 2%
B.
 2.02%
C.
 4%
D.
 4.04%

Explanation:

100 cm is read as 102 cm.

A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.

(A2 - A1) = [(102)2 - (100)2]

= (102 + 100) x (102 - 100)

= 404 cm2.

 Percentage error = 404 x 100 % = 4.04% 100 x 100

12.

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

A.
 75 cu. m
B.
 750 cu. m
C.
 7500 cu. m
D.
 75000 cu. m

Explanation:

1 hectare = 10,000 m2

So, Area = (1.5 x 10000) m2 = 15000 m2.

 Depth = 5 m = 1 m. 100 20

 Volume = (Area x Depth) = 15000 x 1 m3 = 750 m3. 20

Video Explanation: https://youtu.be/dDbVuBzYop8

Direction (for Q.No. 13):

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and

• Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
• Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
• Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
• Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
• Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
13.

 What is the volume of a cube? I. The area of each face of the cube is 64 square metres. II. The length of one side of the cube is 8 metres.

A.
 I alone sufficient while II alone not sufficient to answer
B.
 II alone sufficient while I alone not sufficient to answer
C.
 Either I or II alone sufficient to answer
D.
 Both I and II are not sufficient to answer
E.
 Both I and II are necessary to answer

Explanation:

Let each edge be a metres. Then,

I. a2 = 64       a = 8 m       Volume = (8 x 8 x 8) m3 = 512 m3.

Thus, I alone gives the answer.

II. a = 8 m       Volume = (8 x 8 x 8) m3 = 512 m3.

Thus, II alone gives the answer.

14.

The reflex angle between the hands of a clock at 10.25 is:

A.
 180°
B.
 192 1 ° 2
C.
 195°
D.
 197 1 ° 2

Explanation:

 Angle traced by hour hand in 125 hrs = 360 x 125 ° = 312 1 ° . 12 12 12 2

 Angle traced by minute hand in 25 min = 360 x 25 ° = 150°. 60

 Reflex angle = 360° - 312 1 - 150 ° = 360° - 162 1 ° = 197 1° . 2 2 2

15.

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

A.
 45 min. past 4
B.
 40 min. past 4
C.
 50 4 min. past 4 11
D.
 54 6 min. past 4 11

Explanation:

At 4 o'clock, the hands of the watch are 20 min. spaces apart.

To be in opposite directions, they must be 30 min. spaces apart.

Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

 50 min. spaces are gained in 60 x 50 min. or 54 6 min. 55 11

 Required time = 54 6 min. past 4. 11

16.

A 12% stock yielding 10% is quoted at:

A.
 Rs. 83.33
B.
 Rs. 110
C.
 Rs. 112
D.
 Rs. 120

Explanation:

To earn Rs. 10, money invested = Rs. 100.

 To earn Rs. 12, money invested = Rs. 100 x 12 = Rs. 120. 10

Market value of Rs. 100 stock = Rs. 120.

17.

In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

A.
 32
B.
 48
C.
 36
D.
 60
E.
 120

Explanation:

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

(1) (2) (3) (4) (5) (6)

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.

Number of ways of arranging the vowels = 3P3 = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of these arrangements = 3P3 = 3! = 6.

Total number of ways = (6 x 6) = 36.

18.

Two dice are tossed. The probability that the total score is a prime number is:

A.
 1 6
B.
 5 12
C.
 1 2
D.
 7 9

Explanation:

Clearly, n(S) = (6 x 6) = 36.

Let E = Event that the sum is a prime number.

 Then E = { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),       (5, 2), (5, 6), (6, 1), (6, 5) }

n(E) = 15.

 P(E) = n(E) = 15 = 5 . n(S) 36 12

19.

An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

A.
 21.6 m
B.
 23.2 m
C.
 24.72 m
D.
 None of these

Explanation:

Let AB be the observer and CD be the tower.

Draw BE CD.

Then, CE = AB = 1.6 m,

BE = AC = 203 m.

 DE = tan 30° = 1 BE 3

 DE = 203 m = 20 m. 3

CD = CE + DE = (1.6 + 20) m = 21.6 m.

Direction (for Q.No. 20):
Find the odd man out.
20.

1, 4, 9, 16, 23, 25, 36

A.
 9
B.
 23
C.
 25
D.
 36

Explanation:

Each of the numbers except 23, is perfect square.