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The cost of fuel for running the engine of an army tank is proportional to the square of the speed and Rs. 64/hour for a speed of 16 kmph. Other costs amount to Rs. 400/hour. The tank has to make a journey of 400 km at a constant speed.

Q.

Common Information Question: 1/2

The most economical speed for this January is:

 A.

10 kmph

 B.

20 kmph

 C.

35 kmph

 D.

40 kmph

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Solution:
Option(D) is correct

Cost of fuel is proportional to square of the speed:

\(E=KS^2\)

\(\Rightarrow E=64 \text{ and } S=16 \)

\(K=\dfrac{1}{4}\)

Total cost 

\(=\dfrac{1}{4}\times S^2t+400t\)

Most economical speed, checking options we get most economical speed at 40km/hr.

Edit: A typo has been corrected in the question after it has been pointed out by Sai Rajesh.


(2) Comment(s)


Sai Rajesh
 ()

Please correct "Rs. 64 hour" to Rs. 64 per hour or Rs. 64 / hour & similarly "Rs. 400 hour" to Rs. 400 per hour or Rs. 400 / hour.


Deepak
 ()

Thank you Sai Rajesh for pointing it out, corrected the typo.