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 ?
[amp_mcq option1=”300″ option2=”400″ option3=”460″ option4=”500″ correct=”option2″]
This question was previously asked in
UPSC CAPF – 2017
Given: M = 25%, E = 12%, B = 10%.
The percentage of candidates who failed in at least one subject is given by the formula:
P(M U E) = P(M) + P(E) – P(M ∩ E)
Percentage failed in at least one subject = 25% + 12% – 10% = 37% – 10% = 27%.
The percentage of candidates who passed in both subjects is the remaining percentage:
Percentage passed in both = 100% – Percentage failed in at least one subject = 100% – 27% = 73%.
We are given that 292 candidates passed in both subjects.
Let T be the total number of candidates.
So, 73% of T = 292
(73 / 100) * T = 292
T = (292 * 100) / 73
T = 29200 / 73
Dividing 29200 by 73: 292 / 73 = 4 (since 73 * 4 = 292).
So, 29200 / 73 = 400.
The total number of candidates is 400.