Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

Answer: Option C

Explanation:

\begin{aligned}
Speed = \frac{Distance}{Time} \\
Distance = 750 meter \\
Time = \text{2 min 30 sec} = 150 sec \\
Speed = \frac{750}{150} = 5 m/sec \\

=> 5*\frac{18}{5} km/hr = 18 km/hr
\end{aligned}

Answer: Option B

Explanation:

\begin{aligned}
Speed = \left(80*\frac{5}{18}\right) m/sec \\
= \frac{200}{9} m/sec \\
= 22\frac{2}{9} m\sec
\end{aligned}

Answer: Option D

Explanation:

Let the duration of the flight be x hours.
Then
\begin{aligned}
\frac{600}{x}-\frac{600}{x + \frac{1}{2}} = 200 \\
\frac{600}{x}-\frac{1200}{2x+1} = 200 \\
x(2x+1) = 3 \\
2x^2 + x - 3 = 0 \\
=> (2x+3)(x-1)=0

\end{aligned}
Neglecting the negative value for x we get x = 1

Answer: Option D

Explanation:

We need to calculate the distance, then we can calculate the time and finally our answer.
Lets solve this,

Let the distance travelled by x km
Time = Distance/Speed

\begin{aligned}
\frac{x}{10} - \frac{x}{15} = 2 \\
\text{[because, 2 pm - 12 noon = 2 hours]} \\

3x - 2x = 60 \\
x = 60.

Time = \frac{Distance}{Speed} \\
Time @ 10km/hr = \frac{60}{10} = 6 hours

\end{aligned}
So 2 P.M. - 6 = 8 A.M
Robert starts at 8 A.M.

He have to reach at 1 P.M. i.e, in 5 hours

So, Speed = 60/5 = 12 km/hr

Answer: Option D

Explanation:

We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.

\begin{aligned}
Speed = 5* \frac{5}{18} = \frac{25}{18}m/sec \\
Time = 15*60 seconds = 900 seconds \\

Distance = Time * Speed \\
Distance = \frac{25}{18}*900 = 1250 meter
\end{aligned}