$37\frac{1}{2}\%$ of the candidates in an examination were girls. $75\%$ of the boys and $62\frac{1}{2}\%$ of the girls passed, and 342 girls failed. The number of boys failed was

Explanation

(453) ## Page 2 $$37\frac{1}{2}\% = \frac{3}{8}$$ Let Total student in the class = 800 Total Student (800) Girls $\quad$ Boys $37\frac{1}{2}\% = \frac{3}{8}$ $\quad$ $\frac{5}{8}$ 300 $\quad$ 500 Pass $\quad$ Fail $\quad$ Pass $\quad$ Fail $62\frac{1}{2}\% = \frac{5}{8}$ $\quad$ $= 75\%$ $300 \times \frac{5}{8}$ $\quad$ $= \frac{3}{4}$ $\quad$ $300 \times (1-\frac{5}{8})$ $\quad$ $125 \times 3$ $\quad$ 125 $\quad$ $= 300 \times \frac{3}{8}$ $\quad$ $= 375$ According to the question $300 \times \frac{3}{8} \rightarrow 342$ Now failed boys- $125 \rightarrow 125 \times 342 \times \frac{8}{3 \times 300}$ $\rightarrow 5 \times 342 \times \frac{2}{9}$ $\rightarrow 5 \times 38 \times 2$ Number of boys failed = 380 boys LCM of 4, 5 and 6 = <table> <tr> <th></th> <th>2</th> <th>4,</th> <th>5,</th> <th>6</th>