In a combined test in English and Physics; 36% candidates failed in English; 28% failed in Physics and 12% in both; find :

(i) the percentage of passed candidates.

(ii) the total number of candidates appeared, if 208 candidates have failed.

(i) Percentage of candidates failed only in English = 36% - 12% = 24%

Percentage of candidates failed only in Physics = 28% - 12% = 16%

Percentage of candidates failed in both subjects = 12%

Total failed candidates = 24% + 16% + 12% = 52%

Total passed candidates = (100% - 52%) = 48%

The percentage of passed candidates = 48%.

(ii) Let the total number of candidates be $x$.

Percentage of failed candidates = 52%

Given, 208 candidates failed,

∴ 52% of $x$ = 208

⇒ $\dfrac{52}{100} \times x = 208$

⇒ $\dfrac{13}{25} \times x = 208$

⇒ $x = \dfrac{208 \times 25}{13}$

⇒ $x = \dfrac{5200}{13}$

⇒ $x = 400$

Hence, total number of candidates = 400.