P’s 1 day’s work =1/8

Q’s 1 day’s work =1/12

R’s one day’s work =1/24

Let the number of days taken be x

Then,

x/6+(x-1)/12+(x-2)/24=1

7x-4 = 24

x = 4 days.

Let the tank be full in x minutes

9 minutes 15 seconds = 9.25 minutes

Therefore,

(x-9.25)/18+x/24+x/32=1

16x – 148+12x + 9x = 288

37x = 436     =>x=11.78~12

X=12 minutes.

Pipe A can fill the tank when its efficiency is 100% =40×40/100=16 hours

Pipe B can fill the tank in 48 hours.

When both the pipes operate simultaneously.

Time =(48×16)/(48+16)=12 hours.

Let initially 100 units of work were done by 100 workers in 1 day, so efficiency of each worker was 1%

Now the work becomes 180 units.

So, they need to complete 180 units of work in 1 day.

So, the 100 workers do the 100 units of work

The remaining x new workers need to this 80 units of work in 1 day whose efficiency is 200%each

So, number of new workers needed =80/2=40 newworkersneeded.

So, percent by which workers need to be increased =40/100×100=40%

Both X and Y can do work in 45 days.

So work done in 1 day =1/45 th work

In 10 days, work done =1/45×10=2/9 work

In 12 days, work done by X alone =1-2/9=7/9 work

In 1 day , X can do =7/(9×12)=7/108     =>108/7=15 3/7

So, days X will take to complete whole work = 15 3/7 days

Volume of water collected in the tank in 1 hour

0.4×0.3×30×1000=3600 cubic meter

If after t hours, the water is at height of 6m,

3600t=300×250×6

t = 125 Hours.

As given in the question,

1/A=1/20;

1/B+1/C=1/8;

1/B+1/C+1/A=1/8+1/20=7/40;

In 40 hours, working together, they will complete 7 products.

Thus, in 120 hours they will complete 21 products.

From the question,

(3 men+3 women)×6 days =(4 men +5 women)×5 days.

18 men days +18 women days =20 men days +25 women days

⇒2men days =7women days

⇒ total work,

=18 men days +18 women days

=18×(7/2) womendays+18 womendays

= 63 women days +18 women days

=81 women days

Time taken by 1 women is 81 days

Let us assume some time l.c.m. (30, 60)min=60 min

Now in 30 min time cold water pipe will fill the bath 60/30=2 times whereas hot water pipe will fill it  60/60=1 times.

So in 60 min time bath will be filled 2+1=3 times.

So emptied bath will be fully filled in 60/3=20 min time if waste pipe is closed.

Initially waste pipe is opened, after 20 mins is passed and waste pipe is closed it takes 10 more minutes to fill the bath fully.

So waste pipe has emptied the  10/20=1/2 part of bath in 20 mins.

Rest  1/2 part of tank can be emptied by the waste pipe in  20/2=10 mins.

So waste pipe would empty the tank in 20+10=30 mins

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

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

Fraction of work completed by John Glenn 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 in one day  = 1/25+1/30=11/150

Number of days after day 2 to complete work = (14/15)/(11/150)=140/11  days

So after 2+162/11  =14 8/11  days works will be completed.