The number of red, blue, and green marbles in a bag is in the ratio 4:7:9. If 20 red marbles, 14 blue marbles, and an unknown number of green marbles are added to the bag, the new ratio becomes 5:8:11. Find the number of green marbles added.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 38.
Let original marbles: Red = 4k, Blue = 7k, Green = 9k
(4k + 20)/(7k + 14) = 5/8
⇒ 32k + 160 = 35k + 70
⇒ 3k = 90
⇒ k = 30
Original marbles: Red = 120, Blue = 210, Green = 270
Let the number of green marbles added = x
(270 + x)/(120 + 20) = 11/5
⇒ 270 + x = 308
⇒ x = 38