In a combined test in Maths and Chemistry, 84% candidates passed in Maths, 76% in Chemistry and 8% failed in both. Find :

(i) the percentage of failed candidates.

(ii) if 340 candidates passed in the test, then, how many candidates had appeared in the test ?

(i) Percentage of candidates passed in Mathematics = 84%

Percentage of candidates failed in Mathematics = (100% - 84%) = 16%

Percentage of candidates failed only in Mathematics = 16% - 8% = 8%

Percentage of candidates passed in Chemistry = 76%

Percentage of candidates failed in Chemistry = (100% - 76%) = 24 %

Percentage of candidates failed only in Chemistry = 24% - 8% = 16%

Percentage of candidates failed in both subjects = 8%

Percentage of failed candidates = 8% + 16% + 8% = 32%

The percentage of failed candidates = 32%.

(ii) Percentage of passed candidates = (100% - 32%) = 68%

Given, 340 candidates passed,

∴ 68% of $x$ = 340

⇒ $\dfrac{68}{100} \times x = 340$

⇒ $\dfrac{17}{25} \times x = 340$

⇒ $x = \dfrac{340 \times 25}{17}$

⇒ $x = \dfrac{8500}{17}$

⇒ $x = 500$

Hence, total number of candidates appeared = 500.