Question : If $\tan (x + y)=1$ and $\cos (x-y)={\frac{\sqrt3}{2}}$, then what is the value of $x$ and $y$?

Option 1: $x = 3^\circ, y = 4.5^\circ$

Option 2: $x = 37.5^\circ, y = 7.5^\circ$

Option 3: $x = 7.5^\circ, y = 37.5^\circ$

Option 4: $x = 4.5^\circ, y = 3^\circ$

Question : Anuj's efficiency is 150 percent of Vinod's efficiency. If Anuj can complete a work in 20 days, then how many days will they together take to complete the same work?

Option 1: 6 days

Option 2: 9 days

Option 3: 15 days

Option 4: 12 days

Question : If $x(x+y+z)=20$, $y(x+y+z)=30$, and $z(x+y+z)=50$, then the value of $2(x+y+z)$ is:

Option 1: 20

Option 2: –10

Option 3: 15

Option 4: 18

Question : A and B together can complete a work in 20 days. B and C together can complete the same work in 15 days. If A, B, and C all work together, then the same work gets completed in 10 days. How many days will A and C together take to complete the same work?

Option 1: 8 days

Option 2: 10 days

Option 3: 15 days

Option 4: 12 days

Question : If $x+y+z=13$ and $x^2+y^2+z^2=69$, then $xy+z(x+y)$ is equal to:

Option 1: 70

Option 2: 40

Option 3: 50

Option 4: 60