Problem Solving

20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, afterwhich they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total does the bag currently hold?

Choices:
A 40
B 200
C 380
D 400
E 3200

[spoiler]OA: D. [/spoiler]

Ans : In second attempt 20 marbles pulled out. It contained 1 black marble. So % of black marble in second pull is 5%.

Since there are 20 black marble in back and the percentage of black marbles pulled out the second time represents their actual percentage in the bag.

Hence 20 = 5%of total marbles.
therefore total marbles = 400
Ans (D) 400

from the first statement you know that you had 20 black marbles.

In the second statement 1/20 marbles were black and you are told that this is the same ratio as the black marbles in the bag - thus 1/20 marbles in the bag are black. you know that there are 20 black marbles so 1/20(marbles) = 20 thus marbles = 400 and D is the answer.