Aptitude model placement papers with solution - set 4

ANSWER: B. 30 seconds

Solution:

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: C. 22.5 days

Let us assume that Arnesh finishes his work in 1 day. According to the question, Bhanu will take 3 days to finish the same work. Therefore, there is a difference of two days between the two if Bhanu finishes the work in 3 days.

If the difference is 60 days, then Bhanu will take 3/2 * 60 days, that is 90 days.

Amount of work Bhanu does in 1 day = 1/90

Amount of work Arnesh does in one day is thrice that of Bhanu, that is 3*(1/90)
= 1/30

Amount of work they do together is in one day is 1/90 + 1/30 = 2/45.

Thus, they take total 45/2 days to complete the entire work.

Therefore the answer is 22.5 days.

ANSWER: B. 3:4

Solution:
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: B. 6240

Solution
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: B. 620

Solution:

Let price of one apple be A and price of one orange be B.

According to question, 80A=120B

solving, 2A=3B

B=2A/3 equation 1

Price of 60 apples and 75 oranges is Rs 1320.

This can be represented as 60A+75B=1320

Solving, 4A+5B=88

Substituting for B from equation 1, 4A+5 (2A/3) =88

12A+10A=88*3

diving both sides by 2,

6A+5A=44*3

11A=44*3

diving both sides by 11,

A=12

B= 2A/3, B= 8

Total price of 25 apples and 40 oranges= 25A+40B

That is 25*12+40*8, solving, 300+320

Thus the total price is Rs 620.

ANSWER: B. 4636

Solution

Let the amount be Rs 100.

Simple interest is Rs 80 as the 80% increase is due to simple interest.

Rate of interest= 100 * SI%* time

Solving, rate= 100*80%*8= 10% per annum

Compound interest on a sum of Rs 14000 after 3 years ar 10% rate :

Amount = P(1+rate*100) * time

= 14000 (1*10%)*3
=18634
CI= amount-P
= 18634-14000=4636

Therefore, the compound interest is Rs 4636.

ANSWER: A. 2 years

Solution

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.

ANSWER: B. 3

Solution: To solve this problem a logarithmic identity needs to be kept in mind:
i.e. log_ax + log_ay = log_axy

=> log₁₀5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1 can be written as:

=> log₁₀ (5(5x + 1)) = log₁₀ (10(x +5)) (Taking 1 = log₁₀10)

=> log (25x + 5) = log (10x + 50)

Taking antilog both sides:
5(5x + 1) = 10(x + 5)

=> 5x + 1 = x + 5

=> 3x = 9

=> x = 3

ANSWER: B. 196

Solution
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: A. 42,33

Solution

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.