# Aptitude model placement papers with solution - set 4

## Aptitude model placement papers with solution - set 4

Q1. A man walks with 3kmph speed in the direction of a train. How much time will a 500m long train take to overtake him at a speed of 63kmph?

A. 42 seconds
B. 30 seconds
C. 50 seconds
D. 36 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.

Q2. Arnesh is thrice as good as Bhanu in a work. He finishes a work in 60 days less than that taken by Bhanu. How many days will they take to complete the work together?

A. 18 days
B. 15 days
C. 22.5 days
D. 16 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.

Q3. Find the ratio of speed of truck to train if truck covers 550m in 1 minute and train covers 33 km in 45 min.

A. 4:3
B. 3:4
C. 2:1
D. 1:2

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

Q4. What investment must be made to obtain Rs 650 income from 10% stock at Rs 96?

A. 3100
B. 6240
C. 6000
D. 3500

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.

Q5. 60 apples and 75 oranges together cost Rs 1320. Cost of 80 apples is equal to that of 120 oranges. What will b the price of 25 apples and 40 oranges?

A. 660
B. 620
C. 820
D. 780

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.

Q6. An amount on simple interest over 8 years earns 80% increase. At the same rate, what will be the compound interest on a sum of Rs 14000 in 3 years?

A. 4612
B. 4636
C. 3794
D. 3714

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.

Q7. What time will be taken by an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A. 2 years
B. 1 years
C. 3 years
D. 4 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.

Q8. Find the value of x if:

Log105 + log10 (5x + 1) = log10 (x + 5) + 1

A. 1
B. 3
C. 10
D. 5

Solution: To solve this problem a logarithmic identity needs to be kept in mind:
i.e. logax + logay = logaxy

=> 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

Q9. Which is the odd number?

1, 8, 27, 64, 125, 196, 216, 343

A. 64
B. 196
C. 216
D. 1

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.

Q10. 2 students gave an examination. One of them scored 9 marks more than other and his marks were 56% of the sum of total of both their marks. What are their individual marks?

A. 42,33
B. 42,36
C. 44,33
D. 44,36

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.