The number of marbles in three bags is in the ratio of 2 : 3 : 4. If 12 marbles are added to each bag, then the ratio changed to 8 : 11 : 14. The total number of marbles in the beginning was:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 162.
Let the original numbers of marbles in the three bags = 2x, 3x and 4x
After adding 12 marbles to each bag = 2x + 12, 3x + 12 and 4x + 12
The new ratio is 8 : 11 : 14.
So
(2x + 12) / (3x + 12) = 8 / 11
⇒ 11(2x + 12) = 8(3x + 12) ⇒ 22x + 132 = 24x + 96 ⇒ 132 - 96 = 24x - 22x
⇒ 36 = 2x ⇒ x = 18
So original marbles;
2x = 36
3x = 54
4x = 72
Total = 36 + 54 + 72 = 162