eshwarjayanth wrote:"Randy's" bar serves customers every weeknight from 5 pm to 1 am. In Randy's bar "Silvermoon" beer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.

If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?


(1) Monday, 7:30 pm

(2) Monday, 9 pm

(3) Monday, 7 pm

(4) Monday, 6:45 pm

(5) Monday, 9:30 pm


OA - A

Let the keg = 18 units.
1/2 empty at 5pm = 9 units.
2/3 empty at 6:30pm = 1/3 full = 6 units.
Thus, from 5pm-6:30pm, the amount sold = 9-6 = 3 units.
Since 3 units are sold in 1.5 hours, the regular selling rate = 1 unit per half hour.
Triple the selling rate = 3 units per half hour = 6 units per hour.
Thus, from 6:30-7:30pm, 6 units are sold, emptying the keg by 7:30pm.

The correct answer is A.

At 5:00 p.m. keg is left with (1/2)*x
At 6:30 p.m. keg is left with (1/3)*x

So in 1.5 hours, total beer served = ((1/2)*x) - ((1/3)*x) = (1/6)*x.
So in 1 hour, total beer served = ((1/6)*x)/1.5 = (1/9)*x

Rate of serving during happy hour = 3*(Rate of serving during unhappy hour)= 3*(1/9)*x = (1/3)*x

We know that at 6:30 p.m. keg is left with (1/3)*x, we also know that the happy hour starts at 6:30 p.m and that the rate of serving during happy hour = (1/3)*x, which implies that the Keg would be empty at the end of happy hour - 7:30 p.m [spoiler]Ans :(1) Monday, 7:30 pm [/spoiler]