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?

Answer :

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
$$\begin{gathered} \Rightarrow \frac{1}{55} + \frac{1}{x} = \frac{1}{22} \\ \Rightarrow \frac{x+ 55}{55x} = \frac{1}{22} \\ \Rightarrow 22x+ 1210 = 55x \\ \Rightarrow 33x = 1210 \\ \Rightarrow x = \frac{1210 }{33} \\ \Rightarrow x = \frac{110 }{3} \end{gathered}$$
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)