CAT Questions

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50                           40

Difference = 20kms

Relative Speed = 50 – 40 = 10 kmph

Time = 20/10 = 2 hours.

Given word is THERAPY.

Number of letters in the given word = 7

These 7 letters can be arranged in 7! ways.

Number of vowels in the given word = 2 (E, A)

The number of ways of arrangement in which vowels come together is 6! x 2! ways

Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.

I = PTR/100
I = 25 x 4 x 0.03/100
I = 0.03 x 100 = 300 Ps = Rs. 3

Let the distance and original speed be 'd' km and 'k' kmph respectively.

d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3

=> (5d - 4d)/4k = 1/3 => d = 4/3 k

Time taken to cover the distance at original speed

= d/k = 4/3 hours = 1 hour 20 minutes.

Here the letters follow the rule (AxZ)+(A+Z)

The number corresponding to the letters are used in the rule

A=1, Z=26 => 26x1 + 1 + 26 = 26+27 = 53 =  053

(LxP)+(L+P) = (12 x16) + 12 + 16 = 192+28 = 220

Similarly (11x12) + 11 + 12 => 132 + 23 = 155 

A Match stick. 

You tear a match out of a matchbook and scratch the head to light it, then the red tip turns black from the flame.

Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
(x/2) * (1/15) = 1 => x = 30 min.

From the given options, Though is the only word which gives sense for the sentence. Hence, Though pompous he was an entertaining person.