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Question Detail
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.?
- 9 km/hour
- 10 km/hour
- 11 km/hour
- 12 km/hour
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
1. A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
- 16 km
- 14 km
- 12 km
- 10 km
Answer: Option A
Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4
So distance traveled on foot = 4(4) = 16 km
2. The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
- 10 am
- 11 am
- 12 pm
- 1 pm
Answer: Option B
Explanation:
Suppose they meet x hrs after 8 a.m.
then
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
So, 60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
3. A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 7:30 am. They shall first cross each other at ?
- 7:15 am
- 7:30 am
- 7: 42 am
- 7:50 am
Answer: Option C
Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 7:30 + 12 mins = 7:42
4. A man is walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge is
- 1000 meters
- 1050 meters
- 1200 meters
- 1250 meters
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}
5. A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist
- 16 km/hr
- 17 km/hr
- 18 km/hr
- 19 km/hr
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}
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