Averages

[shashwats]

A certain mixture of nuts consists of 4 parts almonds to 1 part walnuts, by weight. By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight. What percent of the almonds were removed?
(A) 10%
(B) 12.5%
(C) 20%
(D) 25%
(E) 30%

[Anju@Gurome]

A certain mixture of nuts consists of 4 parts almonds to 1 part walnuts, by weight. By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight. What percent of the almonds were removed?

Let us assume initially there was 100 gm of nuts.
So, there was 100*4/(4 + 1) = 80 gm almonds and (100 - 80) = 20 gm walnuts.

Let us assume x gm of walnut was removed.
So, in the remaining mixture, there is (80 - x) gm almonds and 20 gm walnuts.

So, 20/(100 - x) = 25/100 = 1/4
--> (100 - x) = 80
--> x = 100 - 80 = 20

So, 20 gm almonds was removed.
--> 20 = (20/80)*100 % of 80 = 25% of 80

The correct answer is D.

[srcc25anu]

Let Total Mixture be 100
Almonds = 4/5 * 100 = 80
Nuts = 1/5 * 100 = 20
If we remove Y amount of nuts, Nuts / Total Mixture ratio becomes 75%
Lets plug in answer choices to see what results.

A. we remove 10% or 8 units of almonds.
Now ALMONDS to Total % = (80-8) or 72 / 92 NOT EQUAL TO 75%

C. we remove 20% or 16 units of almonds
Almonds / Total = 64 / 86 (NOT EQUAL TO 75%)

D. lets remove 25% of almonds or 20 units
Almonds / Total = 60 / 80 or 3/4 or 75% (CORRECT ANSWER)

[fifafreak]

Almonds = 80; Walnuts = 20

80 + 20 = 100....[1]
80-x + 20 = 100-x ...[2]

[80-x]/[100-x]= 75/100 => x = 20 which is 25% of 80. Ans. D

[GMATGuruNY]

A certain mixture of nuts consists of 4 parts almonds to 1 part walnuts, by weight. By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight. What percent of the almonds were removed?
(A) 10%
(B) 12.5%
(C) 20%
(D) 25%
(E) 30%

Let number of almonds = 4 and the number of walnuts = 1.
After some of the almonds are removed, the remaining almonds must constitute 75% of the remaining total.
Thus, the number of walnuts must constitute 25% = 1/4 of the remaining total.
Thus, after the almonds are removed, the total number of nuts = 4, so that walnuts/total = 1/4.
Since the total number of nuts decreases from 5 to 4, only 1 almond was removed.
Thus:
(almonds removed)/(original number of almonds) = 1/4 = 25%.

The correct answer is D.