Question : P and Q, starting simultaneously from two different places, proceed towards each other at a speed of 20 km/h and 30 km/h, respectively. By the time they meet each other. Q has covered 36 km more than P. The distance (in km) between the two places is:
Option 1: 144
Option 2: 162
Option 3: 180
Option 4: 108
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Correct Answer: 180
Solution : Let P and Q meet after t hours. Distance = Speed × Time Speed of P = 20 km/h Speed of Q = 30 km/h Distance covered by Q in t hrs = 30t Distance covered by P in t hrs = 20t According to the question, 30t – 20t = 36 ⇒ 10t = 36 ⇒ t = $\frac{36}{10}$ = 3.6 hours. $\therefore$ Distance between P and Q = 30t + 20t = 50t = (50 × 3.6) km = 180 km. Hence, the correct answer is 180.
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