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Arithmetic: Time Speed Distance Test-6

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Question 1
A pilot flies an aircraft at a certain speed for a distance of 800 km. He could have saved 40 min by increasing the average speed of the plane by 40 km/h. Find the average speed of the aircraft.
A
200 km/h
B
300 km/h
C
240 km/h
D
None of these
Question 1 Explanation: 
Let the average speed of the aircraft = s km/h
Distance = 800 km
Therefore time taken by the aircraft (t) = 800/s……………………………1
According to question, he could have saved 40 min by increasing the average speed of the plane by 40 km/h
So we can say that
(t - 2/3) = 800/(s+40)…………………………………………………2
From both the equations we can say that
800/s = 800/(s+40) + 2/3
Solving for s, we get
s = 200 km/h
Question 2
An Auto travels 10 km/h faster than a Scooty for a journey of 1000 km. The Scooty takes 5 h more than the Auto to complete the journey. Find the speed of the Scooty.
A
40 km/h
B
70 km/h
C
50 km/h
D
None of these
Question 2 Explanation: 
Let us assume that the speed of the scooty = s km/h
Therefore time taken by the scooty = 1000/s………………………………1
Speed of auto = s + 10
We are given that: the Scooty takes 5 h more than the Auto
So we can say that
1000/(s+10) = (1000/s) - 5………………………………………….2
Using the options in to solve this equations, we see option (a) fits perfectly.
Question 3
If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?
A
11 km/hr
B
12 km/hr
C
13 km/hr
D
14 km/hr
Question 3 Explanation: 
Let’s suppose that the time taken by man at 10km/h to cover the distance by 1 pm = t h
Now at speed of 15km/h the time taken = (t-2) h
Now the distance covered is same so we can say that
10(t) = 15(t-2)
t= 6
Therefore the distance covered will be = 10 x 6 = 60
Therefore the speed at which the man has to travel to reach the place at noon = 60/(t-1) = 60/5 = 12 km/h
Question 4
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/h. The other one walks at 5.4 km/h. The train needs 8.4 and 8.5 s respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A
66 km/h
B
72 km/h
C
78 km/h
D
81 km/h
Question 4 Explanation: 
Let’s suppose that the speed of the train be =  s km/h
We are given the information that both the persons are walking in the same direction of the train
So (s – 4.5)x 8.4 = (s – 5.4)x 8.5
0.1s = 8.1
S= 81 km/h
Question 5
Two trains move from station Ladii and station Pamma towards each other at the speed of 50 km/h and 60 km/h. At the meeting point, the driver of the second train felt that the train has covered 120 km more. What is the distance between Ladii and Pamma ?
A
1320 km
B
1100 km
C
1200 km
D
960 km
Question 5 Explanation: 
At the meeting point, the driver of the second train felt that the train has covered 120 km more.
So if the distance travelled by train from Laddi = d km
Then the distance travelled by from Pamma = (d+120) km
Since the time for both the trains are same so we can say that d/50 = (d+120)/60
by solving this we will get the distance (d) = 600
so the total distance covered by the train = d + (d+120)= 1320 km
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