The total number of students in three classes of an Engineering Institute is 885. The strength of the students in the first two classes are in the ratio of 4 : 9. The ratio of the number of students in the second and the third classes is 6 : 11. How many students are there in the class that has the maximum number of students?

The strength of the students in the first two classes are in the ratio of 4 : 9.

first class : second class = 4 : 9    Eq.(i)

The ratio of the number of students in the second and the third classes is 6 : 11.

second class : third class = 6 : 11    Eq.(ii)

Multiply Eq.(i) by 2 and Eq.(ii) by 3.

first class : second class : third class = $$4\times2 : 9\times2 : 11\times3$$

= 8 : 18 : 33

The total number of students in three classes of an Engineering Institute is 885.

maximum number of students in the class = $$\frac{885}{\left(8+18+33\right)}\times\ 33$$

= $$\frac{885}{59}\times33$$

= 495