The cost of running a bus from A to B , is ₹ (a v+ b v ) , where v ~km / h is the average speed of the bus. When the bus travels at 30 ~km / h , the cost comes out to be ₹ 75 while at 40 ~km / h , it is ₹ 65 . Then the most economical speed (in km / h ) of the bus is :

Step-by-step solution

Let cost C =a v+ b v According to given question, aligned & 30 a+ b 30 =75 & 40 a+ b 40 =65 aligned On solving (i) and (ii), we get a= 1 2 and b=1800 Now, C=a v+ b v aligned & d C d v =a- b v^2 & d C d v =0 a- b v^2 =0 & v= b a = 3600 & v=60 kmph aligned