Aptitude model placement papers with solution - set 9

ANSWER: A. 453600

Solution: This is a simple problem of permutation and combination.

Let us consider the number of times each alphabet is being used:

E: 2
N: 1
C: 2
Y: 1
L: 1
O: 1
P: 1
A: 2
I: 1
D: 1

Now, total number of consonants: 7

=> Total number of vowels: 6
13 letter word ENCYCLOPAEDIA has 6 vowels and there are 6 even spaces

=>6 vowels can be arranged in 6 spaces in ⁶C₆*6!/(2!*2!) ways.

=>Rest of the letters (consonants) can be arranged in 7 spaces in ⁷C₇*(7!/2!) ways

Hence total number of cases: 6!*7!/(2!*2!*2!)

=>Answer: 453600

ANSWER: C. 9/19

Solution: There are a total of 20 balls out of which 2 balls are to be randomly selected

=> There are a total of 10 black and 10 white balls so one can either get 2 black balls or 2 white balls.

=> Number of cases in which both balls are of same color: 10C2 (Black) + 10C2 (White)

=> Total number of cases: ²⁰C₂

=> Probability = (²⁰C₂ + ²⁰C₂)/ ²⁰C₂

=>Answer: 9/19

ANSWER: C. 2:1:3

Solution: Volume of a sphere= (2/3) πr³

Volume of a cone= (1/3) πr²h

Volume of a cylinder= πhr²

Given: Height and radius of all the shapes are same:

Hence, volume of sphere is 4/3πr³

Volume of a cone = (1/3) πr³

Volume of a cylinder = πr³

Ratio: Sphere: Cone: Cylinder

=> 2/3: 1/3: 1

=>2:1:3

ANSWER: C. 3.3222

Solution: By logarithmic properties we know that:

Log_a b = 1/log_ba

So, it is pretty evident that reciprocal of the value of log₁₀2 is:

=>1/.3010 = 3.3222

This is the value of log₂10.

ANSWER: D. Rs 480

Solution: Given data:

Time(t) = 2 years

Rate(R) = 12.5%

Compound Interest = 510 Rs

Let the principal amount be X

Formula for total amount is: = X(1+R/100) ^t

=> 510 = X(1+12.5/100) ²—X

=>X=510*64/17

=>X=1920 Rs

Now, Simple Interest can be calculated by the formula:

SI = (X*R*t)/100

SI= Rs 1920*25/200

SI = Rs 480

ANSWER: A. 1:6

Solution: To start off this question let us assume that cost price of 1 litre milk is Rs 1

Now need to make a mixture and sell this mixture at 1 Rs per litre such that the total gain on mixture is 16.667%.

Therefore, CP of 1 litre of mixture becomes (quantity of milk)/ (quantity of mixture containing 1 L milk)*(price of 1 litre milk).

=>(100/(100+50/3))*1

=>CP of 1 litre milk of mixture: Rs 5/6

As price of any amount of water is zero, and as 1 litre milk costs Rs 1.5/6litre of mixture will comprise entirely of cost of milk which means,1 litre of mixture will contain 5/6th amount of milk.

=>Water is added in the ratio of (1-5/6)=1/6

ANSWER: B. 150 m

Solution: Let us assume for this question that the length of train is x metres and it is assumed to be running at the speed of y m/sec.

A pole is assumed as a point object.

=>Time taken by the train to pass the pole= x/y

=>15=x/y

=>y=x/15

Now, the train passes the platform which is 100 m in length in 25 seconds.

=>x+100/y=25

=>x+100/25=y

Equating speed generated from both cases:

x+100/25=x/15

Therefore x = 150 metres.

ANSWER: B. 6

Solution: The question is based on efficiency to do work.

Ram can finish a puzzle in 3 hours. Shyam can finish the puzzle in 2 hours.

=>In one hour Ram can finish 1/3rd of a puzzle

=>In one hour Shyam can finish half the puzzle

A total of 15 candies are to be shared amongst both of them

Hence Ram’s share must be = ((Work done by Ram in 1 hour)/(Work done by Shyam in one hour)+(Work done by Ram in hour))*15

=> 1/3/((1/2)+(1/3))*15

=> (1/3/(5/6))*15

=> 6/15*(15)

=>6 candies

ANSWER: D. Rs 12,628

Solution: For a given business profit is directly dependent upon the capital invested and the time of investment.

=> Ratio of shares of Akash and Akshay becomes: (35,000*8)/(42,000*10) = 2/3
=>% of profit belonging to Akash: 2/(3+2)*(31,570)
=>Rs 12,768

ANSWER: B. 2

Solution: It is asked in the question that we need to find the number which when subtracted by 14,17 and 34,42 respectively will give their remainders in same ratio.
Mathematically this can be represented in this form:

=> (14-x)/(17-x) = (34-x)/(42-x)

=> Applying Componando &Dividendo

=> C/D = (C+D)/(C-D)

=> (31-2x)/(-3) = (76-2x)/(-8)

=> 248-16x = 228-6x

=>20=10x

=>2=x