CAT Questions

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The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.

Let the present ages of Mahesh, Nilesh and Ramesh be k, l and m respectively.
k/l = 5/x ------ (1)
k = m - 18 ------ (2)
m + 9 = 47 ------ (3)
k - l = m ----- (4)
(3) => m = 47 - 9 = 38 years
(2) => k = 38 -18 = 20 years
(1) => 20/l = 5/x => l = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5

Both warmth and moisture reduce the density of air and hence its pressure is high.

As month begins on Saturday, so 2nd, 9th, 16th, 23rd, 30th days will be Sundays. While 8th and 22nd days are second Saturdays. Thus, there are 7 holidays in all.

Hence, no. of working days = 30 – 7 =23

Let the time taken by train be 't' hrs.

Then,

40t = 35t + 1560

40t = 35t + 35/4

t = 7/4 hrs

Therefore, Required length of the total journey d = s x t

= 40 x 7/4

= 70 kms.

Here in the above given question, the mistake is "the is reapeated twice" before mistake.

Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively.
Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr.
Also, 6x = 72 => x = 12 km/hr
Therefore, the average speed of the car and train together is = 5x+9x2= 7x = 7 x 12 = 84 km/hr.