– The mass of the person $m = 74 text{ kg}$

– The height of a step $h = 20 text{ cm}$

– The number of steps he climbs $N = 100$

Since the metabolic efficiency is $100%$ the work the person does is the same as the amount of energy he spends.

We write:

$$
begin{equation*}
Q = m , g , H
end{equation*}
$$

Where $H = N cdot h = 100 cdot 20 text{ cm} = 20 , text{m}$

So we find the energy:

$$
begin{align*}
Q &= m , g , H = 75 text{ kg} cdot 9.81 frac{m}{s^2} cdot 20 text{ m} \
Q &= 1.45 cdot 10^4 text{ J}
end{align*}
$$

Converting this into calories we have:

$$
begin{align*}
Q = 1.45 cdot 10^4 text{ J} cdot frac{1 text{ C}}{4186 text{J}} = 3.463 text{ C}
end{align*}
$$

– The mass of the barbell $m = 6.2text{ kg}$

– The distance lifted each time $h = 0.58text{ m}$

– The energy burned off $Q = 150text{ C}$

Since the metabolic efficiency is $100%$ the work the person does is the same as the amount of energy he spends.

We write:

$$
begin{equation*}
Q = m , g , H
end{equation*}
$$

Where $H = N cdot h$

We have:

$$
begin{align*}
Q = m , g , N , h
end{align*}
$$

So we express the number of reps:

$$
begin{align*}
N = frac{Q}{m , g , h} = frac{150text{ C}}{6.2text{ kg} cdot 9.81frac{m}{s^2} cdot 0.58text{ m}}
end{align*}
$$

Converting Calories to Joules $1text{ C} = 4186text{ J}$

$$
begin{align*}
N = frac{150 cdot 4186text{ J}}{6.2text{ kg} cdot 9.81frac{m}{s^2} cdot 0.58text{ m}} approx 17800
end{align*}
$$