Option B. 41
Here n(H) = $\frac{120}{2}$ = 60, n(G) = $\frac{120}{5}$ = 24, n(PS) = $\frac{120}{7}$ = 17 [ taking quotient only]
n($H\cap G$) = $\frac{120}{10}$ = 12, n($H\cap PS$) = $\frac{120}{14}$ = 8, n($G\cap PS$) = $\frac{120}{35}$ = 3
n($H\cap G\cap PS$) = $\frac{120}{70}$ = 1
Using Venn Diagrams
Number of student opt for any of three subjects = n( H ∪ G ∪ PS ) = n(H) + n(G) + n( PS ) – n( H ∩ G ) – n ( G ∩ PS ) – n ( PS ∩ H ) + n (H ∩ G ∩ PS)
= 60 + 24 + 17 – 12 – 8 – 3 + 1 = 79
Hence, Number of student opt for none of three subjects = 120 – 79 = 41