MAT Exam 2020 Paper

Concept:For two persons moving to and fro between two fixed points, the total distance covered by both up to the $n$th meeting follows a fixed pattern. The meeting position is found from the remainder when the distance covered by one person is divided by $2D$.Explanation:At the first meeting, A covers $0.4D$ and B covers $0.6D$.Therefore, the ratio of their speeds is $A : B = 0.4 : 0.6 = 2 : 3$.To reach the fourth meeting, the total distance covered by both together is $D + 3 \times 2D = 7D$.Out of this total, A covers $\frac{2}{5}$ of the distance.So, distance covered by A up to the fourth meeting is $\frac{2}{5} \times 7D = 2.8D$.Since one complete round from P to Q and back to P is $2D$, divide $2.8D$ by $2D$.The remainder is $0.8D$, which gives the distance from P.Answer:The fourth meeting occurs at a distance of $0.8D$ from P, so option A is correct.