The students in three batches of BBA are in the ratio 2:3:5. If 20 students are increased in each batch, the ratio changes to 4:5:7. The total number of students in the three batches taken together, before the increase, is__________.

Correct option is C

Given:
The students in three batches of BBA are in the ratio 2 ∶ 3 ∶ 5. If 20 students are increased in each batch, the ratio changes to 4∶5∶7. 
Solution:
Let the common ratio be Q.
The number of students in three batches of BBA is 2Q, 3Q, and 5Q respectively.
Total number of students in the three batches before the increase
⇒ 2Q + 3Q + 5Q
⇒ 10Q
Taking first and second batches,
According to the question,
(2Q + 20)/(3Q + 20) = 4/5
⇒ (2Q + 20) × 5 = (3Q + 20) × 4
⇒ 10Q + 100 = 12Q + 80
⇒ 12Q - 10Q = 100 - 80
⇒ 2Q = 20
⇒ Q = 20/2
⇒ Q = 10
Now, 10Q
⇒ 10 × 10
⇒ 100
The total number of students in the three batches taken together, before the increase is 100.