A bag contains red, blue, and green balls in the ratio 4:5:6. If 6 red balls are removed and 3 green balls are added, the new ratio becomes 2:5:7. How many red balls were originally in the bag?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 12.
Let original red = 4x, blue = 5x, green = 6x
After change: red = 4x – 6, blue = 5x, green = 6x + 3
New ratio (4x – 6) : 5x : (6x + 3) = 2 : 5 : 7
From red/blue: (4x – 6)/(5x) = 2/5
⇒ 5(4x – 6) = 10x
⇒ 20x – 30 = 10x
⇒ 10x = 30
⇒ x = 3
Original red = 4x = 12