Multiple choice

Rakesh travels from A to B at a speed of x kmph and then rests at B for x hours. Again, he travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C and reaches D in 16 hours. If distances A to B, B to C, and C to D are all equal to 12 km, the time for which he rested at B is

  1. 3 hours

  2. 6 hours

  3. 2 hours

  4. 4 hours

  5. 8 hours
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A Correct answer
AI explanation

The time taken to travel the 12 km from A to B at x kmph is 12 divided by x hours, and the time to travel from B to C at 2x kmph is 12 divided by 2x, which equals 6 divided by x hours. The time to travel from C to D at twice the previous speed of 4x kmph is 12 divided by 4x, equaling 3 divided by x hours. Using the equation for the total time, (12/x) plus x plus (6/x) plus 2x plus (3/x) equals 16, simplifying to 3x plus (21/x) equals 16, which yields a rest time x of 3 hours.

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