The students in three batches of a dance class are in ratio 2 : 3 : 5. If 20 students increase in each batch the ratio changes to 4 : 5 : 7. Find the total number of students in the three batches before the increase.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 100.
Let the original number of students in the three batches = 2x, 3x, and 5x
After increasing 20 students in each batch, the new numbers = 2x + 20, 3x + 20, 5x + 20
According to the question, these are in the ratio 4 : 5 : 7, so:
The first two ratios = (2x + 20)/4 = 3x + 20
⇒ 5(2x + 20) = 4(3x + 20)
⇒ 10x + 100 = 12x + 80
⇒ 100 − 80 = 12x − 10x
⇒ 20 = 2x ⇒ x = 100/10 - 80 = 12x - 10x
⇒ 20 = 2x ⇒ x = 10
Original batch sizes:
2x = 20
3x = 30
5x = 50
Total = 20 + 30 + 50 = 100