In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination ?

To find the total number of candidates, we apply the inclusion-exclusion principle for sets. The percentage of candidates who failed in at least one subject is calculated by adding the failure rates of Mathematics (25%) and English (12%) and then subtracting the percentage who failed in both (10%) to avoid double-counting. This results in a total failure rate of 27% (25% + 12% - 10% = 27%). Consequently, the percentage of candidates who passed in both subjects is 73% (100% - 27%). Given that 292 candidates passed in both subjects, we set up the equation 0.73x = 292, where x is the total number of candidates. Solving for x gives 292 / 0.73, which equals 400. Thus, the total number of candidates who appeared in the examination is 400.