Question

There are 40 girls and 60 boys in the class. Their physical education instructor wants to divide them into groups with the equal number of girls and boys in every group. How many maximum groups will he form? Also, how many girls will be their in each group?

• A. $20$ groups
• B. $2$ girls in each group
• C. $12$ groups
• D. $20$ girls in each group

Answer 1

Answer: (A), (B)

$2$ girls in each group

Number of Girls in the class $=40$
Number of Boys in the class $=60$

Maximum groups to be formed by physical education instructor will be GCD of number of Girls and Boys
$\Rightarrow$GCD $(40,60)$
$40=2\times 2\times 2\times 5$
$60=2\times 2\times 3\times 5$

GCD will be $2\times 2\times 5=20$

Maximum $20$ groups will be there.

Now, The number of girls in each group will be $=\frac{40}{20}=2$