Four friends X, Y, Z, and W each have some marbles. X gives Y as many marbles as he already has, gives Z twice the amount of marbles Z already has, and gives W thrice the amount of marbles W already has. Then, W gives 1/6th of his marbles to Y. Afterward, X gives 10% of the marbles he now owns to Z and 20% to Y. Finally, all of them have 50 marbles each. What was the original number of marbles each friend had?
Show answer & explanation
Correct answer: D
Explanation
In the final stage, X gave 10% of his holdings to Z and 20% to Y.
That is, X gave away a total of 30%; therefore, X was left with 70% = 50.
X's holdings prior to this stage = 50 / 0.7 = 500/7.
Y received 20% = (20/100) × 500/7 = 100/7.
Y's holdings prior to this stage = 50 − 100/7 = 250/7.
Z received 10% = 50/7.
Z's holdings prior to this stage = 50 − 50/7 = 300/7.
W remained unchanged in this stage = 50.
Now, in the previous stage, W gave 1/6th of his marbles to Y.
Y's holdings after this transaction = 250/7.
Y's holdings prior to this transaction = 250/7 − (1/6)W.
W's holdings after this transaction = 50.
W's holdings prior to this transaction = 50 × 6/5 = 60.
So, W gave 10 marbles to Y.
Y's holdings prior to this transaction = 250/7 − 10 = 180/7.
Now, prior to the first stage:
X gave Y a number equal to Y's current holdings, gave Z a number equal to 2Z, and gave W a number equal to 3W. That is:
Y doubled ⇒ Original Y = (180/7)/2 = 90/7
Z tripled ⇒ Original Z = (300/7)/3 = 100/7
W quadrupled ⇒ Original W = 60/4 = 15
Total contributed by X = 90/7 + 200/7 + 45
= 290/7 + 315/7
= 605/7
X after the first stage = 500/7
Original X = 500/7 + 605/7 = 1105/7
X = 1105/7, Y = 90/7, Z = 100/7, W = 15