# Two bikers P and Q start their journey of 100 km from the opposite point with speeds of 50 km/h and 40 km/h respectively. Q started 30 minutes after P

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Two bikers P and Q start their journey of 100 km from the opposite point with speeds of 50 km/h and 40 km/h respectively. Q started 30 minutes after P. P, on reaching the destination, turns back and meets Q. How much time does P take to meet Q?

1.

2 h 16 min 40 s

2.

2 h 26 min 40 s

3.

1 h 56 min 40 s

4.

1 h 26 min 40 s

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Correct Answer - Option 2 :

2 h 26 min 40 s

Given:

Speed of P = 50 km/h

Speed of Q = 40 km/h

Distance = 100 km

Formula Used:

Speed = Distance/Time

Concept Used:

If two objects are moving with speeds S1 and S2 in the opposite direction

Their relative speed is S1 + S2

Calculation:

Time taken by P to reach the destination = 100/50 = 2 h

Q starts after 30 min, therefore, distance covered by Q in 1 h 30 min = 40 × 1.5 = 60 km

Now, A turns back.

Distance to be covered by both to meet = 100 – 60 = 40 km

Relative speed = 50 + 40 = 90 km/h

Time = 40/90 km = 4/9 × 60 min = 26 min 40 s

Total time taken by P = 2 h + 26 min 40 s

⇒ 2 h 26 min 40 s

P takes 2 h 26 min 40 s to meet Q.