Multiple choice

Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

  1. 14

  2. 12

  3. 16

  4. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Anil's speed be x and Sunil's speed be y. They meet in 1.5 hours, so 1.5(x+y) = 45, meaning x+y = 30. Anil takes 45/x hours and Sunil takes 45/y hours. We are given 45/x = 45/y + 1.25. Solving these simultaneously with y = 30-x leads to a quadratic equation, yielding x = 12.

AI explanation

Using the relation speed equals distance divided by time, the sum of their speeds is 45 km divided by 1.5 hours, which equals 30 km/h. The product of their individual times to complete the full journey is equal to the product of the sum of their times and the difference in their times, which gives the equation 1.25 times the sum of their times equals 3.75. Solving this reveals that the sum of their total travel times is 3.75 divided by 1.25, equating to exactly 3 hours. Substituting this into the speed sum equation gives the speeds as 18 km/h and 12 km/h, and since Anil takes longer, his speed is 12 km/h.

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