Question : S alone can do a piece of work in 14 days. T alone can do the same work in 21 days. U alone can do the same work in 28 days. Working together, in how many days will they complete the work?

Option 1: $\frac{84}{13}$ days

Option 2: $\frac{77}{13}$ days

Option 3: $\frac{71}{13}$ days

Option 4: $\frac{87}{13}$ days

Question : A alone can complete a work in 16 days and B alone can complete the same work in 96 days. In how many days both A and B together can complete the same work?

Option 1: $\frac{88}{13}$ days

Option 2: $\frac{96}{7}$ days

Option 3: $\frac{96}{13}$ days

Option 4: $\frac{88}{14}$ days

Question : X alone can finish a work in 18 days, and Y alone can finish the same work in 9 days. If X, Y, and Z together can finish the same work in 4 days, then in how many days Z alone can finish the work?

Option 1: 12 days

Option 2: 10 days

Option 3: 14 days

Option 4: 16 days

Question : Avi alone can do a piece of work in 60 days while Prakash alone can do it in 80 days. In how many days will they finish it together?

Option 1: $\frac{250}{6}$ days

Option 2: $\frac{270}{6}$ days

Option 3: $\frac{240}{7}$ days

Option 4: $\frac{140}{6}$ days

Question : A piece of work can be completed by P and Q together in 24 days, and the same piece of work can be completed by R alone in 60 days. If P and R together can do the same work in 36 days, then find the time taken by Q to complete this piece of work alone.

Option 1: $8\frac{4}{5}$days

Option 2: $29\frac{9}{13}$days

Option 3: $3\frac{6}{7}$days

Option 4: $32\frac{8}{11}$days