Let the total number of girls and boys be G and B respectively.

Given,

Pass percentage of girls = 70%
Pass percentage of boys = 65%
Total pass percentage = 67%

We can write,

\frac{70}{100}G + \frac{65}{100}B = \frac{67}{100}(G+B)

\therefore \frac{35}{100}G + \frac{65}{100}B = \frac{33}{100}(G+B)

On solving the equation, we get,

B = \frac{35}{32}G

Now,

G + B = 750

On substituting the value of B in the above equation, we get,

G + \frac{35}{32}G = 750

On solving the equation, we get

G = 400

Hence, the number of boys that appeared in the examination = B = \frac{35}{32}G = \frac{35}{32} \times 400 = 450

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