Question

A truck is to be driven 300 km on a highway at a constant speed of x kmph. Speed rules of the highway required that

30 £ x £ 60. The fuel costs Rs. 10 per litre and is consumed at the rate of 2 + $\frac { x ^ { 2 } } { 600 }$ litres per hour. The wages of the driver are Rs. 200 per hour. The most economical speed to drive the truck, in kmph is

• A. 30
• B. 60
• C. 30 $\sqrt { 3.3 }$
• D. ) 20 $\sqrt { 3.3 }$

Answer 1

Answer: (B)

60

Answer 2

Time taken by the truck = hours

\ petrol consumed = $\left( 2 + \frac { x ^ { 2 } } { 600 } \right) \frac { 300 } { x }$ litre

\ expenses on traveling

E = 200 × $\frac { 300 } { x } + \left( 2 + \frac { x ^ { 2 } } { 600 } \right) \frac { 3000 } { x }$

= $\frac { 60000 } { x } + \frac { 6000 } { x }$ + 5x

= $\frac { 66000 } { x }$ + 5x

\ $\frac { \mathrm { dE } } { \mathrm { dx } }$ = – $\frac { 66000 } { x ^ { 2 } }$ + 5 < 0 for all x Ī [30, 60]

\ most economical speed is 60 kmph