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Two people A and B start simultaneously from points P and Q towards Q and P respectively. After meeting for the first time, A and B take 8 hours and 18 hours respectively to reach their destination. If A travels at a speed of 96 kmph, find the speed of B.
- a)32 kmph
- b)48 kmph
- c)56 kmph
- d)64 kmph
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two people A and B start simultaneously from points P and Q towards Q...
Let's assume that the distance between points P and Q is D km.
- Meeting for the first time:
When A and B meet for the first time, they have covered a total distance of D km (half of the total distance). Since A travels at a speed of 96 kmph, the time taken by A to cover D km is D/96 hours.
- Time taken by A to reach destination:
A takes 8 hours to reach the destination from the meeting point. So, the time taken by A to cover the remaining distance (D/2) is 8 hours.
- Time taken by B to reach destination:
B takes 18 hours to reach the destination from the meeting point. So, the time taken by B to cover the remaining distance (D/2) is 18 hours.
We can use the formula: Speed = Distance/Time to find the speed of B.
Let's calculate the speed of B:
Speed of A = Distance/Time
96 = D/(D/96)
96 = 96
Speed of B = Distance/Time
Speed of B = D/(D/18)
Speed of B = 18 kmph
So, the speed of B is 18 kmph.
Therefore, the correct answer is option 'D' (64 kmph) as given in the question is incorrect.
- Meeting for the first time:
When A and B meet for the first time, they have covered a total distance of D km (half of the total distance). Since A travels at a speed of 96 kmph, the time taken by A to cover D km is D/96 hours.
- Time taken by A to reach destination:
A takes 8 hours to reach the destination from the meeting point. So, the time taken by A to cover the remaining distance (D/2) is 8 hours.
- Time taken by B to reach destination:
B takes 18 hours to reach the destination from the meeting point. So, the time taken by B to cover the remaining distance (D/2) is 18 hours.
We can use the formula: Speed = Distance/Time to find the speed of B.
Let's calculate the speed of B:
Speed of A = Distance/Time
96 = D/(D/96)
96 = 96
Speed of B = Distance/Time
Speed of B = D/(D/18)
Speed of B = 18 kmph
So, the speed of B is 18 kmph.
Therefore, the correct answer is option 'D' (64 kmph) as given in the question is incorrect.
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Community Answer
Two people A and B start simultaneously from points P and Q towards Q...
When A and B meet for the first time, both of them have travelled for the same time
As a result, the distance covered by them will be equal to the ratio of their speeds
Let the time taken to meet for the first time be ‘T’ hours from the time of the start
A and B would take (T + 8) and (T + 18) hours respectively to cover the entire distance
⇒ Ratio of the total time taken by A and B = (T + 8) : (T + 18)
If the distance is constant, then the speed is inversely proportional to Time
⇒ Ratio of speeds of A : B = (T + 18) : (T + 8)
Given: A’s speed = 96 km/hr
When they meet for the first time, A should have covered (96 × T) kms which is the distance which B will cover in 18 hours
⇒ Ratio of the speeds of A and B = 96 : (96T/18)
⇒ (T + 18) : (T + 8) = 96 : (96T/18)
⇒ (T + 18) : (T + 8) = 18 : T
⇒ (T + 18) × T = (T + 8) × 18
⇒ T2 + 18T = 18T + 144
⇒ T2 = 144
⇒ T = 12 hours
Speed of B = ((96x12)/18) kmph = 64 kmph
∴ Speed of B = 64 kmph
Hence, the correct option is (D).
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