What is the distance between two points A and B (in km)? Which of the following statement (s) is sufficient to give the answer:

I. Travelling at x kmph, time taken to cover 75% of the distance is 3 times more than that of remaining distance.

II. Travelling at y kmph, time taken to cover 25%of the distance is 30 minutes.

III. Travelling at (y-8) kmph, time taken to cover 75% of the distance is 1 hour 36 minutes.

IV Travelling at 3y/4 kmph, time taken to cover entire distance is 2hr 40 minutes.

Solution

1st statement=     total distance =D1+D2 = (3/4)x +(x/4)= x unit Time taken to cover           D1       D2                                              4        1                                                                                           2nd statement     time taken to cover 25%of the distance is 30 minutes. Then, time taken to cover (100%) total distance is = 30 × 4 =120 min= 2 hrs. Distance = time × speed Speed = y kmph D = 2 × y D = 2y 3rd statement time taken to cover 75% of the distance is 1 hour 36 minutes (96 minutes) time taken to cover 25% of the distance is 32 minutes. time taken to cover 100% of the distance (total distance) is 128 minutes (2 hr. 8 min) Distance = time × speed Speed = (y-8) kmph D = (32/15) × (y-8) 4th   statement Travelling at 3y/4 kmph, time taken to cover entire distance is 2hr 40 minutes (160 minutes). Distance = time × speed Speed = 3y/4 kmph D = (3y/4) × (8/3) D= 2y From statement 2nd and 3rd D = 2y D = (32/15) × (y-8) 2y = (32/15) × (y-8)  15y = 16y -128 Y =128 km. From statement 3rd and 4th D = 2y D = (32/15) × (y-8) 2y = (32/15) × (y-8)  15y = 16y -128 Y =128 km.