Aptitude test series Set 1

ANSWER: 169

Explanation:
Solution: In this question the pattern * represents a code.

=> 3² + 4² = 25

=> 6² + 8² = 100

=> 12² + 5² = 169

ANSWER: 6

Explanation:
Solution: It is given that 5/8th of the work is completed in 10 days.

=> Remaining work = 3/8th of total

Applying unitary method:

Total work will be completed in 10 * 8 / 5 days

=> It takes 16 days to complete total work

=> Hence, remaining work days = 16 - 10 = 6 days

ANSWER: 700

Explanation:
A boat travels at the speed of 14 km/hr in still water.

=> Speed of stream = 1.2 kmph

=> Speed of boat downstream becomes 14 + 1.2 = 15.2 kmph

=> Speed of boat upstream becomes 14 - 1.2 = 12.8 kmph

Total time taken in the journey = Journey downstream + Journey upstream

Therefore, 4864(1/12.8 + 1/15.2) = 700 hours

ANSWER: 4% of A

Explanation:
It is given that B measures 20% of A

=> So, 20% of A = B or 20/100 * A = B - (1)

B% of 20= B/100 X 20= 2B/10 ---(2)

=> Now, B% of 20

Substituting (1) in (2) we get

2*(2A/10) / 10= 4A/100

Hence, B% of 20 = 4% of A

ANSWER: 7/8

Explanation:
It is given that 3 coins are tossed simultaneously.

=>Total outcomes when one coin is tossed=2

=>Total outcomes when 3 coins are tossed= 2n = 2 X 2 X 2

=8 outcomes

Favourable outcomes: TTH, THT, HTT, THH, THT,HHT,HHH=7

Therefore, Probability= 7/8

ANSWER: 32m

Explanation:
This is a simple speed time problem. Given conditions:

=>Speed of P= 224/28 = 8m/s

=>Speed of Q=224/32 = 7m/s

=>Difference in time taken = 4 seconds

Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres

ANSWER: 29.16L

Explanation:
In regard to the problem let after n times liquid in the container is x and liquid removed is y

=>Liquid in container= x

=>Liquid removed= y

After one trial, quantity of pure liquid= x- (1-y/x)

After n trials quantity of pure liquid = x - (1 -y/x)n

Therefore, Putting the values ( x = 40L y = 4L N=3) and solving

=> 40- (1-4/40)3

= 29.16L

ANSWER: 16

Explanation:
According to the question let n be the number of articles.

=> Cost price of n articles = n

=> Selling price of n articles = 20

=> Profit % = 25%

=> Profit % = (SP - CP)/CP X 100

Putting the values in the formula

(20-n)/n x 100 = 25

=> 5n/4 = 20

=> n = 16

ANSWER: 75625

Explanation:
This question can be solved by 2 approaches:

=> Direct Multiplication

=> Numerical Operations

Direct multiplication is quite time consuming and involves a lot of calculations. An easier approach is based on numerical operations.

=> 121 x (10/2)⁴ = 121 x 10000/16 = 75625 (Lesser calculations, Saves time)

ANSWER: 52

Explanation:
This question contains two series’ running simultaneously:

=> The numbers in odd places are increasing by 8

2 + 8 = 10

10 + 8 = 18

18 + 8 = 26

=> The numbers in even places are increasing by 15

7 + 15 = 22

22 + 15 = 37

37 + 15 = 52

Therefore, Next number will be 37+15= 52

ANSWER: 5%

Explanation:
Increase in population in 10 years= 262500-175000= 87500

Now, % increase will be increase in (population /original population) * 100

=> 87500/175000*100= 50% increase in population over 10 years

Therefore, Average % increase each year= 50/10= 5%

ANSWER: 22

Explanation:
Every hour the hour hand and minute hand coincide once.

=> Every 12 hours hands should coincide 12 times

But in 11 to 1 the clock hands coincide once only at 12

Hence, in every 12 hours hands coincide 11 times.

Therefore, In 24 hours clock hands coincide 11 x 2 = 22 times.

ANSWER: Saturday

Explanation:
The basic concept in a problem involving days is finding the number of odd days. In 61 days:

=> 7 x 8 + 5 = 5 odd days

=> Monday + 5 days = Saturday

Hence 61 days from today will be a Saturday.

ANSWER: 50 years

Explanation:
According to the question current age of the man is:

1. 125% of his age 10 years ago

2. 83.333% of his age 10 years from now

Let the current age of the man be x.

Therefore, equating the two equations generated:

125/100(x-10) = 250/3(x+10)

x = 50

ANSWER: 30 seconds

Explanation:
Distance to be covered = 500 metres

Effective speed will be equal to difference in the speed of ma and train as they move in opposite directions.

Thus, effective speed = 63kmph-3kmph= 60kmph.

60kmph is equal to 50/3 m/s.

Time = Distance/ Speed

Thus, time taken will be equal to 500/(50/3).

On solving, time = 30 seconds.

Therefore, the train will take 30 seconds to overtake the man.

ANSWER: 3:4

Explanation:
Using the formula, speed=distance/time

Speed of truck = 550/60 m/s

Speed of train= 33000/(45*60) m/s

Ratio of speed of truck to train= (550/60 ) / [33000/(45*60)]
=3:4

Hence, the ratio is 3:4

ANSWER: 6240

Explanation:
Given market value = Rs 96

Required income = Rs 650

We assume the face value to be Rs 100.

To obtain 10% of face value, investment had to be Rs 96. So, in order to receive Rs 650, required investment is:

9.6*650=6240

Thus the investment should be Rs 6240.

ANSWER: 196

Explanation:
The pattern in the given question is 1³, 2³,,3³...

In the series, 196 is not a perfect cube and therefore the odd number.

ANSWER: 42,33

Explanation:
Let marks of one of the students be X.

The marks of the other will be X+9

According to question, X+9 = 56% of X+ (X+9)

Solving, X + 9 = 56/100* (2X + 9)

=> 25X + 225 = 28X + 126

=> 3X = 99

=> X = 33

Marks of one are 33, while of the other are 33+9 = 42.

ANSWER: 2 years

Explanation:
P= Rs 900

Rate = 4.5*

SI= Rs 81

=> SI= Time*P*rate

calculating for rate,

=> Time= SI/rate*P

= 81/4.5%*900

=> 2 years

Thus, it will take 2 years to yield Rs 81.