Multiple choice

Rita and Mona decided to meet at a fast food joint. The fast food joint is located somewhere between their houses. Both of them started at the same time from their respective houses which are 72 km apart. Rita walked at the rate of 4 kmph while Mona covered 2 km in first hour, 2.5 km in second hour, 3 km is third hour and so on. If they reached the fast food joint at the same time, find the distance of fast food joint from Rita`s house.

  1. 30 km

  2. 36 km

  3. 45 km

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mona's distance is an arithmetic progression: 2, 2.5, 3... The sum of n terms is (n/2)(2*2 + (n-1)*0.5). Rita's distance is 4*n. Total distance is 72 km. Solving (n/2)(4 + 0.5n - 0.5) + 4n = 72 leads to 0.25n^2 + 5.75n - 72 = 0. Multiplying by 4 gives n^2 + 23n - 288 = 0. Factoring gives (n+32)(n-9)=0, so n=9. Rita's distance is 4 * 9 = 36 km.

AI explanation

Let the time taken to reach the joint be n hours. Rita covers 4n km, and Mona covers the sum of the arithmetic progression 2 + 2.5 + 3 + ... up to n terms, giving a total distance of 72 km. The sum of Mona's distance is (n/2) multiplied by (2 times 2 plus (n - 1) times 0.5), so we solve 4n plus n/2 times (4 + 0.5n - 0.5) equals 72. Solving 0.25n squared + 7.75n - 72 equals 0 gives n = 9, so Rita traveled 4 times 9, which is 36 km.

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