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A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two cities
- a)100 km
- b)120 km
- c)150 km
- d)180 km
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A car travels from P to Q at a constant speed. If its speed were incre...
Let the distance between two cities = D,
D = x*t (x = usual speed and t is the actual time)
D = (X + 20)*(T -2) and D = (X +30)*(T – 2.5)
Solve the above equation, u will get T = 5 and X = 30, so distance = 30*5 = 150 km
D = x*t (x = usual speed and t is the actual time)
D = (X + 20)*(T -2) and D = (X +30)*(T – 2.5)
Solve the above equation, u will get T = 5 and X = 30, so distance = 30*5 = 150 km
Most Upvoted Answer
A car travels from P to Q at a constant speed. If its speed were incre...
Given:
- A car travels from P to Q at a constant speed.
- If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance.
- It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr.
To find: The distance between the two cities.
Solution:
Let the original speed of the car be 's' km/hr and the distance between P and Q be 'd' km.
Then,
Time taken to travel from P to Q at speed 's' = d/s
Time taken to travel from P to Q at speed 's+20' = d/(s+20) (2 hours lesser than the previous time)
Time taken to travel from P to Q at speed 's+30' = d/(s+30) (2.5 hours lesser than the previous time)
We can write the following equations based on the above information:
d/s - d/(s+20) = 2 ----(1)
d/(s+20) - d/(s+30) = 1/2 ----(2)
Simplifying equation (1), we get:
d = 20s ----- (3)
Substituting equation (3) in equation (2) and simplifying, we get:
s = 50 km/hr
Substituting the value of 's' in equation (3), we get:
d = 150 km
Therefore, the distance between the two cities is 150 km.
Answer: Option (c) 150 km.
- A car travels from P to Q at a constant speed.
- If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance.
- It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr.
To find: The distance between the two cities.
Solution:
Let the original speed of the car be 's' km/hr and the distance between P and Q be 'd' km.
Then,
Time taken to travel from P to Q at speed 's' = d/s
Time taken to travel from P to Q at speed 's+20' = d/(s+20) (2 hours lesser than the previous time)
Time taken to travel from P to Q at speed 's+30' = d/(s+30) (2.5 hours lesser than the previous time)
We can write the following equations based on the above information:
d/s - d/(s+20) = 2 ----(1)
d/(s+20) - d/(s+30) = 1/2 ----(2)
Simplifying equation (1), we get:
d = 20s ----- (3)
Substituting equation (3) in equation (2) and simplifying, we get:
s = 50 km/hr
Substituting the value of 's' in equation (3), we get:
d = 150 km
Therefore, the distance between the two cities is 150 km.
Answer: Option (c) 150 km.
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A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two citiesa)100 kmb)120 kmc)150 kmd)180 kme)None of theseCorrect answer is option 'C'. Can you explain this answer?
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