A man drinks a bottle of beer and proposes to work off it's 460 kj by exercising with a 20-kg barbell. If each lift of the barbell from chest height to over his head is through 60 cm and the efficiceny of his body is 10 percent under these circumstances, how many times must he lift the barbell?

To find out how many times the man must lift the barbell to work off the energy from the beer, we need to calculate the total energy expended in lifting the barbell.

First, let's calculate the energy (E) expended in lifting the barbell per lift:
E_lift = m * g * h

Where:
m = mass of the barbell (20 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height raised (0.6 m)

E_lift = 20 kg * 9.8 m/s^2 * 0.6 m
E_lift ≈ 117.6 joules (J)

Now, we know that the body's efficiency under these circumstances is 10 percent. This means that only 10 percent of the expended energy is used effectively.

Efficiency = 10% = 0.1

So, the effective energy (E_effective) used per lift is:
E_effective = E_lift * Efficiency
E_effective = 117.6 J * 0.1
E_effective ≈ 11.76 J

Next, we need to find out how many joules (J) are in 1 kilojoule (kJ). Since 1 kilojoule is equal to 1000 joules, we have:
1 kilojoule (kJ) = 1000 joules (J)

Now, let's calculate the number of lifts required to work off the energy from the beer:
Number of lifts = Energy from the beer / Effective energy per lift

Given that the energy from the beer is 460 kilojoules (kJ), we convert it to joules (J):
Energy from the beer = 460 kJ * 1000 J/kJ
Energy from the beer = 460,000 J

Number of lifts = 460,000 J / 11.76 J
Number of lifts ≈ 39,115.65

Since we can't have a fraction of lifts, we round up to the nearest whole number:

Number of lifts = 39,116

Therefore, the man must lift the barbell approximately 39,116 times to work off the energy from the beer.