In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all the students is Rs 15,50,000. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is

Let the total number of students who chose science, arts, and commerce streams be $$S$$, $$A$$, and $$C$$, respectively.

We have,

$$S+A+C = 1500$$, such that, $$C = 1500-S-A$$ .....(1)

Also, $$1100S + 1000A + 800C = 15,50,000$$,  which can be simplified by dividing by $$100$$;

$$11S + 10A + 8C = 15500$$ .....(2)

Substituting the value of $$C$$ from equation (1) in equation (2), we have

$$11S + 10A + 8(1500-S-A) = 15500$$

$$\Rightarrow 3S + 2A = 3500$$

Since $$S\leq A$$, the maximum value of $$S$$ (if possible), would occur when $$S=A$$, therefore,

$$5S = 3500$$,  or $$S= 700$$.