GATE2011 AG: GA-9

Question

The fuel consumed by a motorcycle during a journey while traveling at various speeds is indicated in the graph below.

The distances covered during four laps of the journey are listed in the table below

$$\begin{array}{|c|c|}\hline \textbf{Lap}  &  \textbf{Distance} & \textbf{Average Speed}\\ & \textbf{(kilometres)} & \textbf{(kilometres per hour)} \\\hline \textbf{P} & 15 & 15 \\\hline \textbf{Q} & 75 & 45 \\\hline \textbf{R} & 40 & 75 \\ \hline \textbf{S} & 10 & 10 \\ \hline  \end{array}$$

From the given data, we can conclude that the fuel consumed per kilometre was least during the lap

• A. $P$
• B. $Q$
• C. $R$
• D. $S$

Comments

The basis Rules OF speed is

 

Speed = Distance/ time

and According to the Time = Distance / Speed

so check the every option and elinimated and also clear the question ask least fules so answer must be highest time they consume low fuels..

A & D both same 1 False

B  1.65 True.

C is 0.53 false

So Q are correct

Answer 1

The first graph gives the fuel consumption in kilometers per litre for various speeds and at $45$ kmph kilometers traveled per litre is $90$ which is the maximum distance per litre and so at this speed fule consumption per litre is the least.  

Second graph shows that for lap $Q$ the average speed is $45$ kmph and so for lap $Q$ we should have the least fuel consumption per litre.

Correct Answer: B.

Comments

@Arjun but sir that's the maximum value so how does it say it's the least?

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yes. The question is a data interpretation one. Fuel consumption is given in graph 1 interms of milage. I have edited the answer. It should be clear now. No calculation required for this question.

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@Arjun sir, I believe the explanation is ambiguous. distance per kilometer and fuel consumption per litre don’t make sense to me. Shouldn’t these be distance per litre and fuel consumption per kilometer?

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Arjun sir approach is absolutely right bcoz here they are asking about $litre/km$ if they asked that $least$ $fuel$ $consumption $ then this approch will not work

Answer 2

This is not very hard question, You just got to do table like the below (It is 2 mark question )
$$\begin{array}{|c|c|c|c|c|} \hline \textbf{Lap} & \textbf{Distance} &\textbf{Speed} &\textbf{Mileage} &\textbf{Total Petrol used} &\textbf{Fuel Consumed Per KM} \\\hline \text{P} & \text{15} &\text{15} &\text{60} &\text{250 ml} &\text{16.66 ml} \\\hline \text{Q} & \text{75} &\text{45} &\text{90} &\text{833 ml} &\text{11.11 ml}\\\hline \text{R} & \text{40} &\text{75} &\text{75} &\text{533 ml} &\text{13.33 ml} \\\hline \text{S} & \text{10} &\text{10} &\text{30} &\text{333 ml} &\text{33.33 ml} \\\hline \end{array}$$
So, answer is $Q$

You get speed, Mileage, Distance from given diagram. You can easily calculate

Total Petrol used in ltr =  Distance / Mileage

Per Km $\implies$ Petrol Used / Mileage.

Correct Answer: $B$

Comments

it can be directly solved (no need to consider distance traveled in a lap)---    

     fuel consumed per liter in a lap = 1/mileage in that lap

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can someone help me how to calculate mileage from the graph

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This is how unknown entries can be filled for the table:

$P:$

$ 1l\Leftarrow60km$

$?\Leftarrow\ 15km$

$?=0.25l/250ml$

 

$ 0.25/250ml\Leftarrow15km$

$?\Leftarrow\ 1km$

$?=250ml\times \frac{1km}{15km}=16.66ml$

Answer 3

Lap	Distance (kilometer)	Average speed (kilometer/hour)	From Graph Fuel Consumed (kilometer/liters)	Fuel Consumed (Liters/kilometer)
P	15	15	60	0.016
Q	75	45	90	0.011
R	40	75	75	0.013
S	10	10	30	0.033

$\therefore$  Option B. $Q$ is the correct answer.

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Explanation

$P$ covers $15 km$ with an average speed of $15 km/hr.$

From the graph we can see that when speed is $15 km/hr$ then fuel consumed is $60 km/L.$

$\Rightarrow$ For 60 km fuel consumed     = $1$ L

$\Rightarrow$ For 1 km  fuel consumed       = $\frac{1}{60}$ L = $0.016$ L

$\therefore$ Fuel consumed per kilometer for Lap P is  0.016 L/km

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$Q$ covers $75 km$ with an average speed of $45 km/hr.$

From the graph we can see that when speed is $45 km/hr$ then fuel consumed is $90 km/L.$

$\Rightarrow$ For 90 km fuel consumed     = $1$ L

$\Rightarrow$ For 1 km fuel consumed       = $\frac{1}{90}$ L = $0.011$ L

$\therefore$ Fuel consumed per kilometer for Lap Q is  0.011 L/km

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$R$ covers $40 km$ with an average speed of $75 km/hr.$

From the graph we can see that when speed is $75 km/hr$ then fuel consumed is $75 km/L.$

$\Rightarrow$ For 75 km fuel consumed     = $1$ L

$\Rightarrow$ For 1 km fuel consumed       = $\frac{1}{75}$ L = $0.013$ L

$\therefore$ Fuel consumed per kilometer for Lap R is  0.013 L/km

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$S$ covers $10 km$ with an average speed of $10 km/hr.$

From the graph we can see that when speed is $10 km/hr$ then fuel consumed is $30 km/L.$

$\Rightarrow$ For 30 km fuel consumed     = $1$ L

$\Rightarrow$ For 1 km fuel consumed       = $\frac{1}{30}$ L = $0.033$ L

$\therefore$ Fuel consumed per kilometer for Lap S is  0.033 L/km

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$\therefore$ We can conclude that the fuel consumed per kilometer was least during the lap Q.

So Option B is the correct answer.

Answer 4

By taking LCM of Distance traveled we can easily visualize the fuel consumption