Solution:

There are 12 pipes attached to the tank. Let ‘n’ of them be fill pipes. Therefore, there will be 12−n drain pipes.

Each fill pipe, fills the tank in 12 hours. Therefore, (1/12)th of the tank gets filled every hour by one fill pipe.

‘n’ fill pipes will, therefore, fill (n/12)th  of the tank in an hour.

Each drain pipe drains the tank in 24 hours. That is, (1/24)th of the tank gets drained by one drain pipe every hour.

12−n drain pipes, will therefore, drain {12−n}/24 of the tank in an hour.

When all the pipes are open when the tank is empty, it takes 2 hours for the tank to overflow. 

i.e. 1/2 the tank gets filled every hour.Equating the information, we get 

n/12−{12−n}/24=12

⇒  {2n+n−12}/24

=1/2

⇒ 3n−12=12 or 3n=24 or n=8.

Therefore, there are 8 fill pipes and (12−8)= 4 drain pipes.

Solution:

Lets assume some time l.c.m(10, 15)min=30 min

Now in 30 min time cold water pipe will fill the bath 30/10=3 times whereas hot water pipe will fill it 

30/15=2 times.

So in 30 min time bath will be filled 3+3=5 times.

=> So emptied bath will be fully filled in 30/5=6 min time if waste pipe is closed.

Initially waste pipe is opened, after 6 mins is passed and waste pipe is closed it takes 4 more minutes to fill the bath fully.

so waste pipe has emptied the 4/6=2/3part of bath in 6 mins.

Rest 1/3 part of tank can be emptied by the waste pipe in 6/2=3 mins

So waste pipe would empty the tank in 6+3=9 min

Solution:

From the given data we can write that the total work is equivalent to (24×16) Man-Days. Which in turn is equivalent to (32×24) woman-Days. 

Hence 1 Man-Day is equivalent to 2 Woman-Days. 

Let x be the number of additional men required for the last two days’ work

Total work =24×16

⇒ (16 Men +16 Women) × 12-Days +(16 Men +16 Women) × 2-Days

⇒ (16 Men + 16/2 men) × 12-Days +(16 Men + 16/2 men) × 2-Days

= Or, 24×16=24×12+(24+x)×2

⇒ x= 24.

Solution:

Fraction of work completed by Abhinav in one day =1/25

Fraction of work completed by Bipul in one day =1/30

Fraction of work completed by Bipul on day1 and day 2=2(1/30)=1/15

Fraction of work left after 2 days =1−{1/15}=14/15.

Fraction of work completed by Both =1/25+1/30=11/150

Number of days after day 2 to complete work =(14/15)/(11/150)

=12.72 days.

So after 2+13= 15 days works will be completed.

Solution:

Machine I:

Number of nuts produced in one minute = 100

To produce 1000 nuts time required =10 min

Cleaning time for nuts =5 min

Over all time to produce 1000 nuts =15 min.

Over all time to produce 9000=138 min −5 min =133 min -----(1)

Machine II:

To produce 75 bolts time required =1min

To produce 1500 bolts time required =20 min

Cleaning time for bolts =10 min.

Effective time to produce 1500 bolts =30 min

Effective time to produce 9000 bolts =30×6−10=170 min ------ (2)

From (1) and (2)

Minimum time = 170 minutes