One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10.

Remaining Work = 7/10, which was done by A,B and C in the initial number of days. 

Number of days required for this initial work = 7 days. 

Thus, the total numbers of days required = 4 + 7 = 11 days.

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

Take a Look at this series :

23 - 22 =  8 - 4 = 4  

33 - 32 = 27 - 9 = 18 

43 - 42 = 64 - 16 = 48  

53 - 52 = 125 - 25 = 100  

63 - 62 = 216 - 36 = 180 

73 - 72 = 343 - 49 = 294 

83 - 82 = 512 - 64 = 448

Let the numbers be 3x, 4x and 5x.

Then, their L.C.M. = 60x.

So, 60x = 2400 or x = 40.

 The numbers are (3 x 40), (4 x 40) and (5 x 40).

Hence, required H.C.F. = 40.

We know that d=√2s 

Given diagonal = 20 cm 

=> s = 20/2 cm

Therefore, perimeter of the square is 4s = 4 x 20/2 = 402   cm.

First letters are common. Second letters are:b, c, c, c, c. One of the four words having c is the last word. Let us see the third letters now ,there are: t, c, q, h. Clearly t is the last. Hence Actuate is the last word. 

The difference of the two consecutive numbers are 1, 4, 9, 16, 25, 35. 

This is clearly , +12, +22, +32, +42, +52,+62 

Here 35 is wrong, So our wrong number is 91