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A, B and C start from same place X and travel at 25 kmph, 30 kmph and 35 kmph respectively. If B starts 2 hours after A has started, how many hours after B has started should C start, so that both B and C overtake A at the same time.

A, B and C start from same place X and travel at 25 kmph, 30 kmph and 35 kmph respectively. If B starts 2 hours after A has started, how many hours after B has started should C start, so that both B and C overtake A at the same time. Correct Answer 10/7

Solution:

Concept:

Speed = Distance/Time

Given:

Speed of A = 25 kmph

Speed of B = 30 kmph

Speed of C = 35 kmph

B started his journey 2 hours after A start his journey

Calculation:

Let be assume C start his journey Q hours after B has started till then A can cover distance,

= (Q + 2) × 25

When C will start till then B can cover the distance,

= Q × 30

B will have to cover the distance to overtake A = (Q + 2) × 25 -  Q × 30

Relative speed between A and B is = 30 – 25 = 5

So, B will take time to overtake A = {(Q + 2) × 25 – Q × 30}/5 = 10 – Q

C will have to cover the distance to overtake A = (Q + 2) × 25

Relative speed between A and C is = 35 – 25 = 10

So, C will take time to overtake A = (25Q + 50)/10

Now according  to question both will overtake A at the same time then,

10 – Q = (25Q + 50)/10

Q = 10/7

∴ C will start his journey 10/7 hours after B has started. 

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