Multiple choice

Soniya and Priyanka started from Amethi and Bellari , which are 645 km apart. They meet after 15 hours. After their meeting , Sonia increased her speed by 3 km/hr and Priyanka reduced her speed by 3 km/hr, they arrived at Bellari abd Amethi respectively at the same time. What is their initial speed?

  1. $24\ and\ 23$
  2. $21\ and\ 23$
  3. $20\ and\ 23$
  4. $21\ and\ 25$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Their initial speeds add to 645/15 = 43 km/hr. After meeting, the equal-time condition gives p/(s + 3) = s/(p - 3), which simplifies to p - s = 3. Solving s + p = 43 and p - s = 3 gives speeds 20 km/hr and 23 km/hr.

AI explanation

Let the initial speeds of Sonia and Priyanka be x km/hr and y km/hr. Since they meet after 15 hours, the ratio of the distances they covered is x to y, meaning Sonia covered 15x km and Priyanka covered 15y km before meeting. After meeting, Sonia travels the remaining 15y km at a new speed of (x + 3) km/hr, while Priyanka travels the remaining 15x km at a new speed of (y minus 3) km/hr. Because they arrive at their destinations at the same time, the time taken by Sonia equals the time taken by Priyanka, so 15y divided by (x + 3) equals 15x divided by (y minus 3). We also know the total distance is 645 km, so 15x plus 15y equals 645, which simplifies to x plus y equals 43. Solving these equations yields the initial speeds of 20 km/hr and 23 km/hr.

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