In a colony, 68% of the households have a cooking-gas connection and the rest do not. If 216 more households have the connection than do not, how many households are there in the colony?

Those with the connection are 68% and those without are 32%, so the gap is 68 - 32 = 36% of the households. Then 0.36 $xN=216$, giving $N=600$. Check: 408 with and 192 without, and 408 - 192 = 216. 675 divides 216 by 0.32, using one group as the base instead of the gap between the groups; 408 and 192 are the two groups themselves.