In a class test the average marks of the boys is 64 and that of the girls is 74, while the class as a whole averages 70. If there are 30 girls in the class, how many boys are there?

Each boy is 70 - 64 = 6 marks below the class average and each girl is 74 - 70 = 4 marks above it, and the two must cancel: 6 × (boys) = $4\times 30$, so boys = 120/6 = 20. Check: $(20\times 64+30\times 74)/50=3500/50=70$. 45 pairs each deviation with the wrong group, solving 4 × (boys) = $6\times 30$ - the smaller deviation always belongs to the larger group, so the boys must be fewer than the girls, not more. 30 assumes equal numbers, which would force the class average to be 69. 50 is the class strength, not the number of boys.