Answer: 32 days

Molar mass of butane, $C_4H_10 = 12 \times 4 + 10 = 58 g mol^{-1}$

58 g of butane gives 2658 kJ of heat energy.

$\therefore$ 14 kg of butane will give heat energy = $\frac{2658 kJ \times (14 \times 10^3 g)}{58 g} = 641.5862 \times 10^3 kJ$

Daily energy requirement for cooking = 20,000 kJ = $2 \times 10^4$ kJ $day^{-1}$

$\therefore$ Number of days cylinder will last = $\frac{641.5862 \times 10^3 \text{ kJ }}{2\times 10^4 \text{ kJ }day^{-1}}$ = **32.08 days**