At 12:00 in the afternoon Paul stopped at the gas station and filled his car's 50-liter tank to capacity. After Paul drove 75 miles away from the station, the tank developed a leak and the car started to lose 1/5 liters of fuel per minute. If Paul is traveling at a constant speed of 50 miles per hour and his car consumes 10 liters per every 100 miles, at what time of the day will Paul run out of gas?

A. 4:00 pm
B. 4:15 pm
C. 4:30 pm
D. 5:00 pm
E. 5:20 pm


Source: GMAT Club Tests - Hardest GMAT questions

Answer is (A)
At 12:00 p.m. Paul has 50 liters in his tank. He then starts driving at a speed of 50 mph and after 75 miles there is a leak in his car.

S=Distance/Time
50 = 75/Time
Time = 1.5 hours

So when there is a leak, Paul has already traveled for 1.5 hours. So the time when the tank started leaking, the time is 1:30 p.m.

75*10/100 = 7.5 liters get consumed till 1:30 p.m. as the car ran for 75 miles.
So at 1:30 p.m. there is 50 - 7.5 = 42.5 liters remaining in the fuel tank, since the distance traveled is 75 miles.

Now once the tank started leaking, the car is losing fuel at the rate of 1/5 th liter per minute which is 1 liter in 5 minutes, but at the same time Paul is driving the car as well and the car consumes 10 liters for every 100 miles run.

Speed = 50 miles per hour. So in 2 hours Paul will drive for 100 miles.
So now say it is 3:30 p.m. and Paul has driven for 2 more hours and the car has lost 10 liters + 24 liters (1/5th liter per minute) get consumed till 3:30 p.m.

So remaining fuel in the car is 50 - 7.5 - 10 - 24 = 8.5 liters

Now say, Paul continues driving so till 4:00 p.m. the car consumes 2.5 liters (10 liters for 100 miles so for 25 miles 2.5 liters get consumed) + 6 liters (1/5th liter in 1 minutes, so its 6 liters in 30 minutes) = 8.5 liters

So the car's tank is empty at 4:00 p.m.

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