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A bike running at 80 km/h initially is slowed down to 60 km/h as soon

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nkmungila
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A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   21 Sep 2017, 03:46
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A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. If the bike consumes 2 litres of fuel per hour, what is the capacity (in litres) of the fuel tank of the bike?

(A) 16
(B) 20
(C) 32
(D) 40
(E) 56
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C
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arvind910619
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   21 Sep 2017, 07:18
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Imo C

Let the distance traveled at speed 80 miles\hour be x
then distance traveled at speed 60 miles\hour =640-x
we know the total time =10 hours

So let T1 be time taken to travel x miles at 80 m\h =x\80

T2 be time taken to travel (640-x)\60
Now we have 10=x\80+ (640-x)\60
Solving the above equation we get x=160 so T1 =2 hours
therefore bike traveled 8 hours at speed 60 m\h
We are given that bike starts travelling at 60m\h when the fuel in tank reaches half the value

Rate of burning of fuel =2 litres \hour
Therefore it burnt 16 liters therefore the capacity of the tank is 32 liters
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A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   21 Sep 2017, 15:26
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nkmungila wrote:
A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. If the bike consumes 2 litres of fuel per hour, what is the capacity (in litres) of the fuel tank of the bike?

(A) 16
(B) 20
(C) 32
(D) 40
(E) 56

Answer C.

I think the key is: Half of the fuel is used at 60 km per hour.

When the bike started traveling at 60 km per hour, it started with exactly half a tank of fuel, all of which was used up.

So the segment at 60 km/hr will yield the capacity of the tank.

Fuel consumption rate is given in hours. We need time, in hours, that the bike travels at 60 km/hr.

Total time is 10 hours
Total distance is 640 km

Time for 60 kmh, segment 2, = T

Time for 80 kmh, segment 1 = (10 - T)

Segment 1 (r*t) + Segment 2 (r*t) = Total Distance

80(10 - T) + 60T = 640
800 - 80T + 60T = 640
20T = 160
T = 8

So time taken at 60 km per hour is 8 hours.

Amount of fuel used:
8 hrs * \(\frac{2L}{hr}\) = 16 Liters

16 Liters is only half of the fuel capacity. Full fuel capacity therefore is
16L * 2 = 32 Liters

ANSWER C
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   22 Sep 2017, 21:39
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this is my lazy logic:

Assuming the bike hardly drove in the 80km/h speed, that is, we are assuming the petrol in just half tank. --- we are doing this to get the maximum capacity, but the actual capacity will be less than this.

the bike traveled the 640km in 10 hrs at 60km/h ------- which implies half tank capacity is 20 Ltrs

Therefore, maximum, full tank capacity is 40Ltrs, the only answer between 40 and 20 is 32.. so answer is 32ltrs.

Please point out any flaw in my logic.

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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   25 Sep 2017, 16:37
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nkmungila wrote:
A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. If the bike consumes 2 litres of fuel per hour, what is the capacity (in litres) of the fuel tank of the bike?

(A) 16
(B) 20
(C) 32
(D) 40
(E) 56


We can let the time the bike runs at 80 km/h = h hours, and thus the number of hours the bike runs at 60 km/h = 10 - h hours and we can create the following equation:

80h + 60(10 - h) = 640

80h + 600 - 60h = 640

20h = 40

h = 2

Thus, the bike runs at 60 km/h for 10 - 2 = 8 hours, which will consume 8 x 2 = 16 litres of fuel since the bike consumes 2 litres of fuel per hour. Recall that the bike starts to run at 60 km/h when the fuel tank is half full, so the tank must have 32 litres of fuel when it’s full.

Answer: C
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   26 Sep 2017, 01:49
The question is confusing because it does not specifically state that the given fuel consumption (2L/hr) applies to the second segment of the trip (when it was travelling at 60 km/hr).
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   01 Oct 2017, 04:24
It sates that
" If the bike consumes 2 litres of fuel per hour"
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   04 Nov 2017, 12:52
arvind910619 wrote:
Imo C

Let the distance traveled at speed 80 miles\hour be x
then distance traveled at speed 60 miles\hour =640-x
we know the total time =10 hours

So let T1 be time taken to travel x miles at 80 m\h =x\80

T2 be time taken to travel (640-x)\60
Now we have 10=x\80+ (640-x)\60
Solving the above equation we get x=160 so T1 =2 hours
therefore bike traveled 8 hours at speed 60 m\h
We are given that bike starts travelling at 60m\h when the fuel in tank reaches half the value

Rate of burning of fuel =2 litres \hour
Therefore it burnt 16 liters therefore the capacity of the tank is 32 liters



Hi arvind910619
I've done the same way and it is completely ok, but logically I have a problem
if we know that the trip was 10 hour and that the tank is empty know because all the fuel is used
why it is wrong that 10 houres*2 liters each hour?!
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   04 Nov 2017, 20:34
nkmungila wrote:
A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. If the bike consumes 2 litres of fuel per hour, what is the capacity (in litres) of the fuel tank of the bike?

(A) 16
(B) 20
(C) 32
(D) 40
(E) 56


let t=time at 60 kmh
60(t)+80(10-t)=640 km
t=8 hours
8*2=16 liters=1/2 fuel tank capacity
16*2=32 liters total fuel tank capacity
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink] New post   08 Jul 2023, 12:36
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Re: A bike running at 80 km/h initially is slowed down to 60 km/h as soon [#permalink]
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