In a colony, 55% of the households own a refrigerator, and 40% of those households also own a washing machine. If 264 households own both, how many households are there in the colony?

Households owning both = 40% of 55% = $0.55\times 0.40=22$% of the colony. So 0.22 $xN=264$, giving $N=264/0.22=1,200$. Check: 1200 -> 660 own a refrigerator -> 264 own both. 660 is 264/0.40, which stops one stage early at the refrigerator-owning households; 480 is 264/0.55, dividing by the wrong single share; and 1,320 comes from mis-reading $0.55\times 0.40$ as 0.20.