Question : Dhiru can dig $\frac{1}{a}$ of a field in 20 hours. What fraction of the same field can Kaku dig 20 hours if the two of them can dig the field in 60 hours, working together at their respective rates?

Option 1: $\frac{(a-3)}{a}$

Option 2: $\frac{1}{3a}$

Option 3: $\frac{3a}{(3-a)}$

Option 4: $\frac{(a-3)}{3a}$

Question : A and B working together can do a piece of work in $4\frac{1}{2}$ hours. B and C working together can do it in 3 hours. C and A working together can do it in $2\frac{1}{4}$ hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work.

Option 1: 3 hours

Option 2: 2 hours

Option 3: 2.5 hours

Option 4: 3.25 hours

Question : Reena, Veena, and Vimla can do a work in 4 hours, 8 hours, and 12 hours, respectively. In how much time will they finish the work working together?

Option 1: $\frac{2}{11}$ hours

Option 2: $5\frac{2}{11}$ hours

Option 3: $3\frac{2}{11}$ hours

Option 4: $2\frac{2}{11}$ hours

Question : Two pipes A and B can fill a tank in 6 hours and 8 hours respectively. If both the pipes are opened together, after how many hours should B be closed so that the tank is full in 4 hours?

Option 1: $\frac{2}{3}$ hours

Option 2: $1$ hour

Option 3: $2$ hours

Option 4: $\frac{8}{3}$ hours

Question : If the numerator of a fraction is increased by 60% and the denominator is increased by 40%, then the resultant fraction is $\frac{16}{63}$. The original fraction is:

Option 1: $\frac{5}{9}$

Option 2: $\frac{2}{9}$

Option 3: $\frac{2}{11}$

Option 4: $\frac{4}{9}$

Question : Pipes A, B and C together can fill a cistern in 12 hours. All three pipes are opened together for 4 hours and then C is closed. A and B together take 10 hours to fill the remaining part of the cistern. C alone will fill two-thirds of the cistern in:

Option 1: 60 hours

Option 2: 40 hours

Option 3: 48 hours

Option 4: 50 hours