Question : A can do $\frac{4}{5}$th of a work in 20 days and B can do $\frac{3}{4}$th of the same work in 15 days. They work together for 10 days. C alone completes the remaining work in 1 day. B and C together can complete $\frac{3}{4}$th of the same work in:

Option 1: 6 days

Option 2: 8 days

Option 3: 5 days

Option 4: 4 days

Question : To do a certain task X would take 3 times as long as Y and Z together, and Z would take 4 times as long as Y and X together. Three of them together can complete the task in 10 days. How much time is taken by X and Z to complete the task?

Option 1: $18 \frac{2}{9}$ days

Option 2: $20 \frac{1}{9}$ days

Option 3: $21 \frac{1}{9}$ days

Option 4: $22 \frac{2}{9}$ days

Question : What is $\frac{\left (x^{2}-y^{2} \right)^{3}+\left (y^{2}-z^{2} \right )^{3}+\left (z^{2}-x^{2} \right )^{3}}{\left (x-y \right)^{3}+\left (y-z \right )^{3}+\left (z-x \right)^{3}}?$

Option 1: $\frac{(x+y)(y+z)}{(x+z)}$

Option 2: $(x+y)^3(y+z)^3(z+x)^3$

Option 3: $(x+y)(y+z)(z+x)$

Option 4: $(x+y)(y+z)$

Question : A and B together can do a certain work in $x$ days. Working alone, A and B can do the same work in ($x$ + 8) and ($x$ + 18) days, respectively. A and B together will complete $\frac{5}{6}$th of the same work in:

Option 1: 12 days

Option 2: 8 days

Option 3: 10 days

Option 4: 9 days

Question : Vipin can do a piece of work in 2 days; Vaibhav can do the same work in 3 days and Chirag can do the same work in 6 days. If they start working together, how many days will they take to complete the work?

Option 1: 3

Option 2: 1

Option 3: 5

Option 4: 4