The number of yellow, purple, and orange marbles in a bag is in the ratio 2 : 3 : 5. If 16 yellow marbles, 18 purple marbles, and an unknown number of orange marbles are added to the bag, the ratio of yellow, purple, and orange marbles becomes 4 : 5 : 7. Find the number of orange marbles added.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 22.
Let the initial numbers of yellow, purple, and orange marbles be 2x, 3x, and 5x
Number of orange marbles added = k
From Yellow and Purple: (2x + 16)/(3x + 18) = 4/5
⇒ 10x + 80 = 12x + 72
⇒ 2x = 8
⇒ x = 4
Yellow marbles after addition = 2(4) + 16 = 24
Orange marbles after addition = 5(4) + k = 20 + k
From Yellow and Orange: 24/(20 + k) = 4/7
⇒ 168 = 80 + 4k
⇒ 4k = 88
⇒ k = 22 orange marbles