CAT Questions

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A red ball can be drawn in two mutually exclusive ways

 (i) Selecting bag I and then drawing a red ball from it.

(ii) Selecting bag II and then drawing a red ball from it.

Let E1, E2 and A denote the events defined as follows:

E1 = selecting bag I,

E2 = selecting bag II

A = drawing a red ball

Since one of the two bags is selected randomly, therefore 

P(E1) = 1/2  and  P(E2) = 1/2

Now, PAE1 = Probability of drawing a red ball when the first bag has been selected = 4/7

  PAE2  = Probability of drawing a red ball when the second bag has been selected = 2/6

 Using the law of total probability, we have 

 P(red ball) = P(A) = PE1×PAE1+PE2×PAE2 

                          = 12×47+12×26=1942

SP = Rs.800 ; Profit = 25%

 CP = SP x 100100+P% = 800 x 100100+25 = 640

 Now, CP = Rs.640

Loss = 25% = 25% of Rs.640 = Rs.160

Thus, SP = CP - Loss = Rs.640 - Rs.160 = Rs.480

Poor people have Nothing

Rich people need Nothing

If you eat Nothing you die.

Hence, it is Nothing.

Here in the alphabets the letter U is missing and it represents the word MISSING YOU (U).

Let the cost price of a ball is Rs.x
Given, on selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls
The equation is :
17x - 720 = 5x
Solving the equation
we get x = 60
Therefore, cost price of a ball is Rs. 60.

In the given series numbers are arranged following the rule,

55,44, 33, 22, 11

 Therefore, the missing number is 27.