Two cars 𝐶₁ and 𝐶₂ start simultaneously from two cities 𝑃 and 𝑄, moving towards each other. They meet for the first time 30 km away from 𝑄. After meeting they exchange their speeds as well as the direction in which they were moving and proceed to travel towards their respective starting points. Upon reaching their starting points, they turn back with the same speed and meet for the second time at a point which is 10 km away from 𝑃. Which of the following gives the distance between 𝑃 and 𝑄 (In km)

Let the total distance between P and Q be D and the ratio of their speeds be v1:v2. During the first meeting, the sum of the distances they covered is D, and during the second meeting, the total distance covered by both cars is 3D. This implies that the total time elapsed up to the second meeting is exactly three times the total time elapsed up to the first meeting. At the first meeting, car C1 covered a distance of D - 30, so after tripling this time, the total distance covered by car C1 becomes 3D - 90, which places it exactly 10 km away from P on its return trip, resulting in an equation of 2D = 170.

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