While going to a destination after travelling 75km, the

Solution

Let A is the starting point and B is actual point where bus met with an accident C is the assumed point bus met with an accident Given BC = 15km and Difference of is 30 minutes basically due to the speed covering this 15km. Let original speed = x  km/hr  Speed after clutch problem = (2x)/5  km/hr ⇒  15/((2x)/5)-15/x=30/60 ⇒ 75/(2x)-15/x=1/2 ⇒  (75-30)/(2x)=1/2 ⇒  45/(2x)=1/2 ⇒  x = (45 × 2)/2 x = 45 km/hr  Let the distance be ‘D’ km  Time taken at original speed =D/45  hr……….(i) Time taken after clutch problem took place at 75 km distance = (75/45)+(D-75)/(45×(2/5)` = 75/45+(5(D-75))/(45×2) = 5/3+((D-75))/18 = (30+D-75)/18 = (D-45)/18  ………………………..(ii) As per the question, (ii) – (i) = 5 hours (D-45)/18-D/45=5  = (5D-225-2D)/90=5  = (3D-225)/90=5  3D – 225 = 450  3D = 675      D = 225 km