Question

The students in three classes are in the ratio $2:3:5.$ If $40$ students are increased in each class, the ratio changes to $4:5:7.$ Originally the total number of students was:

• A. $100$
• B. $180$
• C. $200$
• D. $400$

Answer 1

Answer: (C)

$200$

Let the original number of students be $2a:3a;5a$
If $40$ students are increased in each class, the ratio changes to $4:5:7$
$\therefore 2a+40:3a+40:5a+40=4:5:7$
$\therefore \frac{2a+40}{4}=\frac{3a+40}{5}=\frac{5a+40}{7}$
Choosing the first two,
$\therefore \frac{2a+40}{4}=\frac{3a+40}{5}$

$\therefore 10a+200=12a+160$
$2a=40$
$a=20$
Hence, the total number of students originally $2a+3a+5a=10a=10\times 20=200$