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

If you think the solution is wrong then please provide your own solution below in the comments section .

Average monthly salary of labourers and supervisors = Rs 1250
Average monthly salary of supervisors = Rs 2450
Average monthly salary of labourers = Rs 950
Let the number of labourers be 'x' and the number of supervisors be 'y'

Therefore,
Average monthly salary of labourers and supervisors = (950x + 2450y)/(x + y)

On rearranging, we get
950x + 2450y = 1250 (x + y)

Simplifying further, we get
850x = -1200y

Divide both sides by 850
x = -1400/850 y

Since y = 6
Therefore, x = -1400/850 x 6

x = 24

Hence, the number of labourers = 24.

If you think the solution is wrong then please provide your own solution below in the comments section .