Ques1- Alok worked on a set of mathematics problems for 20 min and finished 4/15 of it. He then called Asha. Working together, they finished the complete set in 22min. How long would Asha and Alok alone had taken to finish the set?

Ques2- Pipe A can fill tank in 3hrs. Pipe B can fill tank in 4hrs. An outlet pipe C can empty the tank in 6hrs. If all three pipes are kept open simultaneously, in how many hrs will the tank will be half full?

Ques3- Tap A fills tank in 2hrs. Outlet B and c can empty the tank in 4hrs and 6hrs respectively. If the tank is empty and A and B are turned on, hoe long will it take to fill up? After the tank A,B and C are all turned on. How long will the tank take to be empty?

Ques4- Tap A can fill a tank in 8min. Outlet B can empty the tank in 12min. If both are kept open,how long will it take to fill the tank?

1 ) Remaining task = 1- $\frac{4}{15}$ = $\frac{11}{15}$

$\frac{4}{15}$ task takes time of Alok =20 min

1 task will take time =20 $\times $ $\frac{15}{4}$ = 75 min. (ans)

Both took time to complete $\frac{11}{15}$ task = 22 min

And Alok alone took time to complete $\frac{11}{15}$ task = 75 - 20 = 55 min

Let

Asha alone took time to complete $\frac{11}{15}$ task =

*x*

So

*,*we get

$\Rightarrow \frac{1}{55}+\frac{1}{x}=\frac{1}{22}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x+55}{55x}=\frac{1}{22}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 22x+1210=55x\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow 33x=1210\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{1210}{33}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{110}{3}\phantom{\rule{0ex}{0ex}}$

So,

$\frac{11}{15}$ task takes time of Asha = $\frac{110}{3}$ min

1 task will take time =$\frac{110}{3}$ $\times $ $\frac{15}{11}$ = 50 min. ( Ans )

2 ) Total work done to fill the tank by pipe A and B in 1 hr = $\frac{1}{3}$ +$\frac{1}{4}$ = $\frac{7}{12}$

Work done by pipe C to empty the tank in 1 hr = $\frac{1}{6}$

Work done to fill the tank in 1 hr = $\frac{7}{12}$ -$\frac{1}{6}$ = $\frac{5}{12}$

Work done to fill half tank in 1 hr = $\frac{5}{12}$ $\times $ 2 = $\frac{12}{10}$

So,

Time taken to fill the half tank when all thee pipes open =$\frac{12}{10}$ =1.2 hrs (ans)

3 ) Work done if A and B are open to fill the tank in 1 hr =$\frac{1}{2}$ - $\frac{1}{4}$= $\frac{1}{4}$

Time taken to fill the tank = 4 hrs (ans)

Work done if A, B, and c are open in 1 hr =$\frac{1}{2}$ - $\frac{1}{4}$ - $\frac{1}{6}$ = $\frac{1}{12}$

Time taken to empty the tank = 12hrs (ans)

4 ) Work done by A and B in 1 hr = $\frac{1}{8}-\frac{1}{12}=\frac{1}{24}$

So,

Time taken to fill the tank = 24min (ans)

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