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Kalyani

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· 1 Months ago

alternate solution (Question:921919.0)

why does t has root

Question:

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.

Options:
A)

32 kmph

B)

48 kmph

C)

56 kmph

D)

64 kmph

E)

None of these

Solution:

 

Ans: (d)

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 Speed of B = (Distance/Time) = (96 × T)/18 kmph

⇒ 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 = 1 2 hours

Speed of B = (96 × 12)/18 kmph = 64 kmph

∴ Speed of B = 64 kmph 

Alternate solution: 

\(\cfrac{S1}{S2}=\sqrt{\cfrac{T2}{T1}}\)

\(\cfrac{96}{S2}=\sqrt{\cfrac{18}{8}}\)

\(S2=\cfrac{96\times2}{3}=32\times2=64\cfrac{km}{hr}\)

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