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11. A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work the work together but A left 8 days before the completion of the work and B 12 days before the completion of work. Only C worked up to the end. In how many days was the work completed?

Discuss
Solution:
Let the work be completed in x days. C work for x days then A works for (x - 8) days and B works for (x - 12) days.
According to the question,
x−836+x−1254+x72=16x−48+4x−48+3x216=113x−96=21613x=216+96=312x=31213x=24days
12. While working 7 hour a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, 8 hour a day?

Discuss
Solution:
A can complete the work in 7 × 6 = 42 hours
1 hour's work of A = 142
B can complete the work in 7 × 8 = 56 hours
1 hour's work of B = 156
(A + B)'s 1 hour's work
=142+156=4+3168=7168
∴ Time taken by (A + B) working 8 hours daily
1687×8=3days
13. Two pipes, P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes, P is turned off. In how many more minutes will Q fill the cistern?

Discuss
Solution:
P can fill cistern in 12 minutes
P fills cistern in 1 minute = 112
Q can fill cistern in 15 minutes
Q fills cistern in 1 minute = 115 part
P and Q together can fill cistern in 1 minute,
=112+115⇒960    part
So, they can together fill cistern in 3 minute,
=3×960⇒920    part
Rest Cistern = 1−920  = 1120  part
1120 part cistern must be filled by Q in
1120115=814   minutes

Alternatively,
Pipe P can fill cistern in one minute = 10012 = 8.33%
Pipe Q can fill cistern in one minute = 10015 = 6.66%
(P + Q) together can fill the cistern in one minute = 15%;
In 3 minutes cistern is filled = 45%
P become off, then rest of cistern will be filled by Pipe Q in = 556.66 = 814 minutes.
14. Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all three pipes are open, empty tanks become full in one hour. The capacity of the tank (in gallons) is:

Discuss
Solution:
Let capacity of the tank = x gallons;
Part of the tank filled in 1 minute
=x24+x40−30Or,x24+x40−30=x60Or,x24+x40−x60=30Or,10x+6x−4x240=30Or,12x=30×240Or,x=600gallons
15. A cistern can be filled by two pipes in 20 and 30 minutes respectively. Both pipes being opened, when the first pipe must be turned off so that the cistern may be filled in 10 minutes more.

Discuss
Solution:
% Cistern is filled by 1st pipe in one minute = 10020 = 5%
% Cistern is filled by 2nd pipe in one minute = 10030 = 3.33%
% cistern filled by 1st and 2nd pipes in one minute = 8.33%

According to question,
Cistern is totally filled by 2nd pipe in last 10 minute.
That means 2nd pipe filled 33.3% of the cistern in last 10 minute and 66.66% of cistern is filled by 1st and 2nd pipe together in = 66.668.33  = 8 minutes
Thus, after 8 minute, 1st pipe must be turned off.
16. A tank can be filled with water by two pipes A and B together in 36 minutes. If the pipe B was stopped after 30 minutes, the tank is filled in 40 minutes. The pipe B can alone fill the tank in:

Discuss
Solution:
Let the pipes fill the tank in x minutes.
Part of tank filled by pipes A and B in one minute: 136
Part of the tank filled by pipe A in 1 minute = 136−1x

According to the question,

30×1x+40(136−1x)=1⇒30x+4036−40x=1⇒30x+109−40x=1⇒10x=19
Hence, x = 90 minutes.
Alternatively,
% of tank filled by (A+B) in 1 minute = 10036 = 2.78%
% of tank filled in 30 minutes = 2.78 × 30 = 83%
That means 17% of tank can be filled by A in last 10 minutes
Then, % tank filled by A in 1 minute = 1710 = 1.7%
% of tank filled by B in 1 minute = 2.78 - 1.7 = 1.1%
So, B alone can fill 100% tank in,
= 1001.1 = 90 minutes (approx.)
17. A boy and a girl together fill a cistern with water. The boy pours 4 liters of water every 3 minutes and girl pours 3 litres every 4 minutes. How much time will it take to fill 100 litres of water in the cistern?

Discuss
Solution:
Water filled by (boy + girl) in one minute,
43+34=16+912=2512liter
Hence, time taken to fill 100 liter,
 = 100×1225=48minutes
18. A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minutes in the tank, the leak takes 15 hours to empty the tank. how many litres does the tank hold?

Discuss
Solution:
Let the capacity of the tank = q litres
According to the question,
Quantity of water emptied by the leak in 1 hour = q10 litres
Qunatity of water filled by the tap in 1 hour = 240 litres
According to the question,
⇒q10−q15=240⇒3q−2q30=240⇒930=240⇒q=240×30⇒q=7200litres
19. A, B and C completed a work costing Rs. 1800. A work for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by A?

Discuss
Solution:
Ratio of their daily wages = 5 : 6 : 4
Total wage = Rs. 1800
6 × 5x + 4 × 6x + 4 × 9x = 1800 [As A, B, C works for 6, 4, 9 days respectively]
Or, 90x = 1800
Or, x = 180090
Total amount of A = 1800×3090   = Rs. 600
20. A man and a boy received Rs. 800 as wages for 5 days for the work they did together. The man's efficiency in the work was thrice times that of the boy. What are the daily wages of the boy?

Discuss
Solution:
Man = 3 boy
Daily wages for them = 8005 = 160
4 boy (1 man + 1 boy) = 160
4 boy = 160
Or, boy = Rs. 40

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