Aptitude and Reasoning Questions

Let the ratio of initial quantity of oils be 'x' => 4x, 5x & 8x.
Let k be the quantity of third variety of oil in the final mixture.
Let the ratio of initial quantity of oils be 'y'
From given details,
4x + 5 = 5y ..... (1)
5x + 10 = 7y .....(2)
8x + k = 9y ......(3)

By solving (1) & (2), we get
x = 5 & y = 5

From (3) => k = 5

Therefore, quantity of third variety of oil was 9y = 9(5) = 45kg.

Let A be the event of driver A drive safely after consuming liquor. 

Let B be the event of driver B drive safely after consuming liquor. 

Let C be the event of driver C drive safely after consuming liquor. 

P(A)=2/5,P(B)=3/7,P(C)=3/4

The events A, B and C are independent . Therefore,

PA∩B∩C=P(A)P(B)P(C)=25*37*34=970

Therefore, The probability that all the drivers will drive home safely after consuming liquor is 9/70

For convenience , we assign numbers to each word :

allow  children  to  play  on  the  ground

   1         2      3    4      5    6       7

It has been coded as : 

play  allow  on  children  the  to  ground

  4       1     5        2       6    3      7

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Hence the given code is :

the  do  open  not  electric  touch  wires

 4     1      5     2       6         3       7

Now arranging them as 1 2 3 4 5 6 7, we have "do not touch the open electric wires'.

Hence, option (3) is correct answer. 

6.72/100 = 672/10000 = 42/625

Given Word is PROMISE.

Number of letters in the word PROMISE = 7

Number of ways 7 letters can be arranged = 7! ways

Number of Vowels in word PROMISE = 3 (O, I, E)

Number of ways the vowels can be arranged that 3 Vowels come together = 5! x 3! ways

Now, the number of ways of arrangements so that three vowels should not come together

= 7! - (5! x 3!) ways = 5040 - 720 = 4320.

Let the three numbers be x, y, z.

From the gien data,

x = 2y ....(1)

x = z/2 => z = 2(2y) = 4y .....(From 1)  ...........(2)

Given average of three numbers = 56

Then,

$$\begin{gathered} x + y + z3 = 56 \\ 2y + y + 4y3 = 56 (From 1 & 2) \\ 7y = 56 x 3 \\ y = 24 \end{gathered}$$

Now,

x = 2y => x = 2 x 24 = 48

z = 4y = 4 x 24 = 96

Now, the highest number is z = 96 & smallest number is y = 24

Hence, required sum of highest number and smallest number

= z + y

= 96 + 24

= 120.

Let the selling price of the rice = Rs.P/kg

Now, according to the question,

1040 - 100p = 30p

=> p = 8/kg

Hence, the selling price of the rice = Rs. 8/kg

Because each vertice of the square is the center of a circle
(1/4) part of the total area of each circle inside of the square.
(3/4) part of the total area of each circle outside of the square.
Thus total area outside the square is 434×227×3.5×3.5 = 115.3955 sq cm.