Question

In a school, there are 480 girls and 270 boys. Their auditorium is a little crowded, and so the teachers have to arrange the students in equal rows such that there are an equal number of boys in each of the boy’s row and an equal number of girls in each of the girl’s row. Find the minimum number of rows so that this is possible if no row contains both girls and boys.

• A. 40
• B. 110
• C. 25
• D. 30

Answer 1

The correct option is C

25

Since the number of boys and girls in corresponding boys and girls rows should be equal, we need to make sure that the number of rows in which they are ordered is a common factor of both 480 and 270. To make the arrangement in a least possible area, this common factor should be the highest (The highest common factor)
Step 1 : $480=270\times 1+210$
Step 2 : $270=210\times 1+60$
Step 3 : $210=60\times 3+30$
Step 4 : $60=30\times 2+0$
HCF = 30.
So in each of the boys row, there will be $\frac{270}{30}$ = 9 boys.
And in each girls row, there will be $\frac{480}{30}$ = 16 girls
Therefore, minimum number of rows =25