Ratio of speed of Bus and Train = 15 : 27.
Let speed of the bus is 15X and Speed of the Train is 27X.
Car Covered 720 km in 9 hours.
So, Speed of the Car = 720/9 = 80 kmph.
Given, Speed of the bus is 3/4 of Car, So speed of the Bus,
= (80*3)/4 = 60 kmph.
15X = 60
X = 4
So, Speed of the train = 27X = 27*4 = 108 kmph.
Hence, Train will cover distance in 7 hours,
= 108 * 7 = 756 km.
P__150m___T______X m (Let)_______Q.
Let Policeman caught thief at a distance (X + 150)m. And Thief has traveled X m.
Speed of Policeman = 12 kmph = (12*5)/18 = 60/18 m/sec.
Speed of thief = 10 km = (10*5)/18 = 50/18 m/sec.
In this case time is constant means Policeman covered (X + 150)m in same time thief covered X m.
Speed of the thief /Speed of Policeman = X/(150+X) 50/60 = X/(150+X)
7500 + 50X = 60X
10X = 7500
X = 750 m.
So, Thief has traveled 750 m before the caught.
Let usual speed be X kmph, then new speed will be (X+400)kmph.
Time taken to cover 1600 km with speed X kmph,
Time taken to cover 1600 km with Speed (X+400) kmph,
Time difference = 40 minutes.
(1600/X)-(1600/(X+400)) = 40/60 hours.
X2 +400X - 960000 = 0
X = -1200, 800.
Speed cannot be negative, So usual speed will be 800 km per hour.
He proceeds at 4/5 S where S is his usual speed means 1/5 decrease in speed which will lead to 1/4 increase in time. Now the main difference comes in those 12km (30-18) and the change in difference of time = (45-36) min = 9 min
Thus, 1/4 * T = 9 min where T is the time required to cover the distance of (30 - 18) = 12 km T = 36 min = 36/60 hours = 0.6 hours.