Latest TCS Aptitude Question SOLUTION: Assume that the rate of consumption of coal by a locomotive engine varies as the square of its speed and is 1000 kg per hour when the speed is 60 kmph, when in motion. If coal cost

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(#M40038945) TCS Numerical Ability question time and speed Keep an EYE

Assume that the rate of consumption of coal by a locomotive engine varies as the square of its speed and is 1000 kg per hour when the speed is 60 kmph, when in motion. If coal costs the railway company Rs.15 per 100 kg and if the other expenses of running the train is Rs.12 per hour, find a formula for the cost in paise per kilometre when the speed is S km per hour.
options:
(1200/S)+(25S^2/6)
(1200/S)+(5S^2/18)
(1200/S)+(25S/6)
none

Asked In TCS Niveditha Ravichandran (9 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

RAKESH  (9 years ago)

R = K*S^2
put R=1000, S=60
1000 = k*60^2 => K = 5/18

R = (5/18)*S^2

Total Cost(C) = Coal cost + Other costs =
C = 12*100/S + (5/18 *S^2)/S *15
C = (1200/S) + (25S/6)

Is this solution Helpfull? Yes (57) | No (9)  

SOUMYA SANKAR BAKSHI  (8 years ago)

Let R be the rate of consumption.
Let S be the speed of the engine.
So,by the problem,
R=K*S^2
where K is an arbitrary constant.
When R=1000 kg per hr,S=60 km per hr,
1000=K*60^2
or,K=5/18.
Therefore,R=5/18*S^2
Again,cost of 100 kg=Rs.15
Cost of 1 kg coal=Rs.15/100
cost of R i.e, 5/18*S^2=Rs.(5/18*S^2*15/100)
=(5/18*S^2*15) paise
Cost of coal for S km=(5/18*S^2*15) paise
Cost of coal per km=(5/18*S^2*15/S)
Again,when it is S km,other cost=Rs.12=1200 paise
Other cost per km=(1200/S) paise
Therefore,total cost in paise per km
=(1200/S)+(5/18*S^2*15/S)
=(1200/S)+(25S/6)
Hence,3rd option is the right answer.

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RAKESH  (9 years ago)

C( in paise) = 12*100 + (5/18)*S^2* 15 [for 1 kg coal, 15/100 *100 paise]

C(paise/ km) = 12*100/S + (5/18)*S^2* 15 / S [divide by S]

Is this solution Helpfull? Yes (16) | No (2)  

abhay pandey  (9 years ago)

Ans: 3rd option: (1200/S)+25S/6;
verification:

soln: consuption= (1000*15)/100 =>150
total consumption=150 + extra 12 rupees= 162rupees per 60 km
Rs.per Km= 162/60 =>2.7 rupees per km => 270 paise per km which satisfy the option..

Is this solution Helpfull? Yes (11) | No (4)  

Niveditha Ravichandran  (9 years ago)

@RAKESH
pls explain this step. i dont get this
C = 12*100/S + (5/18 *S^2)/S *15

Is this solution Helpfull? Yes (5) | No (2)  

Vithiya  (9 years ago)

Abhay pandey....y (1000*15)/100 can u pls explain

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hashmi  (9 years ago)

hello rakesh
y 12*100/s

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Pavan  (6 years ago)

@ABHAY PANDEY
How is satisfy the 3rd option

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