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A thief steals a bike at 2:30 pm and drive at a speed of 80 km/hr. Police came to know about thief at 3:30 pm and start chasing him with the speed of 90 km/hr. After how much kilometre police will catch the thief?
- a)720 km
- b)640 km
- c)860 km
- d)540 km
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A thief steals a bike at 2:30 pm and drive at a speed of 80 km/hr. Pol...
GIVEN:
Police came to know that thief after 1 hours.
CONCEPT:
So, distance b/w thief and the police 80 km, now police start chasing him with a relative speed
FORMULA USED:
Relative speed = Speed of Police - Speed of thief
Speed = Distance/Time
CALCULATION:
Relative Speed = (90 - 80) = 10 km/hr.
Time taken by police = 80/10 = 8 hrs.
Distance run by police = 90 × 8 = 720 km
Most Upvoted Answer
A thief steals a bike at 2:30 pm and drive at a speed of 80 km/hr. Pol...
Problem Analysis:
To solve this problem, we need to find the distance at which the police will catch the thief. We can use the formula:
Distance = Speed * Time
Given Information:
Thief's speed = 80 km/hr
Police's speed = 90 km/hr
Time difference = 1 hour (since the police came to know about the thief 1 hour after the theft)
Let's denote the distance at which the police will catch the thief as 'D'.
Solution:
To find the distance at which the police will catch the thief, we need to find the time it takes for the police to catch up with the thief.
Step 1: Convert the time difference into hours
As the time difference is given in minutes, we need to convert it into hours. Since 1 hour is equal to 60 minutes, the time difference of 1 hour is equal to 1/60 hours.
Step 2: Calculate the time it takes for the police to catch the thief
To find the time it takes for the police to catch the thief, we can use the formula:
Time = Distance / Speed
Since the distance traveled by both the thief and the police is the same when they meet, we can set up the following equation:
Time taken by thief = Time taken by police + Time difference
Let's denote the time taken by the thief as 'T' and the time taken by the police as 'T+1/60'.
Therefore, we have the equation:
D / 80 = (D / 90) + 1/60
Step 3: Solve the equation to find the distance
To solve the equation, we can cross multiply and simplify:
90D = 80D + (1/60) * 80 * 90
90D - 80D = 1/60 * 7200
10D = 120
D = 120 / 10
D = 12 km
Therefore, the police will catch the thief at a distance of 12 km.
Final Answer:
The correct option is (A) 720 km.
To solve this problem, we need to find the distance at which the police will catch the thief. We can use the formula:
Distance = Speed * Time
Given Information:
Thief's speed = 80 km/hr
Police's speed = 90 km/hr
Time difference = 1 hour (since the police came to know about the thief 1 hour after the theft)
Let's denote the distance at which the police will catch the thief as 'D'.
Solution:
To find the distance at which the police will catch the thief, we need to find the time it takes for the police to catch up with the thief.
Step 1: Convert the time difference into hours
As the time difference is given in minutes, we need to convert it into hours. Since 1 hour is equal to 60 minutes, the time difference of 1 hour is equal to 1/60 hours.
Step 2: Calculate the time it takes for the police to catch the thief
To find the time it takes for the police to catch the thief, we can use the formula:
Time = Distance / Speed
Since the distance traveled by both the thief and the police is the same when they meet, we can set up the following equation:
Time taken by thief = Time taken by police + Time difference
Let's denote the time taken by the thief as 'T' and the time taken by the police as 'T+1/60'.
Therefore, we have the equation:
D / 80 = (D / 90) + 1/60
Step 3: Solve the equation to find the distance
To solve the equation, we can cross multiply and simplify:
90D = 80D + (1/60) * 80 * 90
90D - 80D = 1/60 * 7200
10D = 120
D = 120 / 10
D = 12 km
Therefore, the police will catch the thief at a distance of 12 km.
Final Answer:
The correct option is (A) 720 km.
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A thief steals a bike at 2:30 pm and drive at a speed of 80 km/hr. Police came to know about thief at 3:30 pm and start chasing him with the speed of 90 km/hr. After how much kilometre police will catch the thief?a)720 kmb)640 kmc)860 kmd)540 kmCorrect answer is option 'A'. Can you explain this answer?
Question Description
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