Explanation :

 B's 1 day's work =1/12-    1/20

=2/60=1/30

 Now, (A + B)'s 1 day's work =1/20+1/60

 =4/60=    1/15

.    [  B works for half day only    ]         

 So, A and B together will complete the work in 15 days.

Explanation :

 Suppose B takes x days to do the work.

  A takes {2 x3/4}x=3x/2

 days to do it.         

 (A + B)'s 1 day's work =    1/18

 1/x=2/3x=1/18

 or x = 30

Explanation :

 (A + B)'s 1 day's work =    1/72

 (B + C)'s 1 day's work =    1/120

 ; (A + C)'s 1 day's work =1/90

 Adding, we get: 2(A + B + C)’s 1 day’s work =1/72+1/120+1/90=12/360=1/30

 (A + B + C)'s 1 day's work =1/60

 So, A’s 1 day’s work =1/60-1/120 =1/120

  A alone can do that work in 120 days.   

At 4:00 , the angle between the 2 hands of the clock the angle is 120 degree.

The minute hands run at 6 degree/minute & the hour hand run at ½ degree per minute .

30 /(6-1/2) = 60/11 = 4:05 :27.

Zero or more Cherries can be selected in 4 + 1 = 5 ways (0 cherry, 1 cherry, 2 cherries, 3 cherries and 4 cherries)

Similarly pomegranates can be selected in 7 +1 = 8 ways

And guavas in 6 +1 = 7 ways

So total number of ways = 5*8*7 = 280

But we included a case of 0 cherry, 0 pomegranate and 0 guava, so we have to subtract this, so 280 – 1 = 279 ways