CAT Questions

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4/3 π x 10 x 10 x 10 = 8 x 4/3 π x r x r x r
r = 5
4π x 5 x 5 = 100π

Days remaining 124 – 64 = 60 days

Remaining work = 1 - 2/3 = 1/3

Let men required men for working remaining days be 'm'

So men required = (120 x 64)/2 = (m x 60)/1 => m = 64

Men discharge = 120 – 64 = 56 men.

Case I :  MW  MW  MW  MW

Case II:  WM  WM  WM  WM

Let us arrange 4 men in 4! ways, then we arrange 4 women in 4P4 ways at 4 places either left of the men or right of the men. Hence required number of arrangements

   4! × 4P4 + 4! × 4P4 = 2 × 576 = 1152

Let the length be 'l' and breadth be 'b'.

b = l × 3/4__________(a)

2(l+b) = 1050

l+b = 525___________(b)

From equations (a) and (b),

l = 300m, b = 225 m

Area = l × b

= 300 × 225

= 67500 sq.m.

x – y = 5

4x – 6y = 6

x = 12 y = 7

Here the given words, sullen and moody are synonyms to each other which means that gloomy, resentful. Similarly, repetitious and monotonous are synonyms to each other which means dull, tedious.

Hence, Sullen : moody :: monotonous : repetitious.

Speed in still water = Average of Speed in Upstream and speed in Downstream

= 1/2 (12 + 6) kmph = 9 kmph.