Question : On day one, with speed $v$, R covers a distance $x$, in t time. On the next day, he covers a distance of 2.5 $x$ in 0.75 $t$ time. What is his speed in the next day?

Option 1: $3.5v$

Option 2: $\frac{10}{3}v$

Option 3: $4.5v$

Option 4: $\frac{5}{3}v$

Question : R jogs at twice the speed of walking and runs at twice the speed of jogging. From his home to office, he covers half of the distance by walking and the rest by jogging. From his office to home, he covers half the distance jogging and the rest by running. What is his average speed (in km/hr) in a complete round from his home to office and back home if the distance between his office and home is 10 km and he walks at the speed of 5 km/hr?

Option 1: $\frac{90}{8}$

Option 2: $\frac{60}{8}$

Option 3: $\frac{60}{9}$

Option 4: $\frac{80}{9}$

Question : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

Option 3: $\frac{7}{2}$

Option 4: $\frac{8}{7}$

Question : If $2\cot x=5$, then what is $\frac{2 \cos x-\sin x}{2 \cos x+\sin x}$ equal to?

Option 1: $\frac{3}{4}$

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

Option 3: $\frac{5}{6}$

Option 4: $\frac{2}{3}$

Question : A car covers a certain distance in 25 hours. If it reduces the speed by $\frac{1}{5}$th, the car covers 200 km less in that time. The speed of the car is:

Option 1: 60 km/hr

Option 2: 30 km/hr

Option 3: 40 km/hr

Option 4: 50 km/hr

Question : R, S, and T can finish a work in 20,15, and 10 days, respectively. R works on all days and S and T work on alternate days with T starting the work on the first day. In how many days is the work finished?

Option 1: $\frac{61}{7}$

Option 2: $\frac{50}{7}$

Option 3: $\frac{52}{7}$

Option 4: $\frac{57}{8}$