One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%
B. 24%
C. 22%
D. 18%
E. 8.5%

I am awful at these but here is what I got

75(0.1) + 25(x) = 100(0.16)
7.5 + 25x = 16
x = 8.5/25 = 0.34

34% it is

Answer A: 34%

Simply,
.75*.1+.25*y = .16
Solving for y would give the value 34%

Explanation:
.75% is still 10% solution
.25% is the y% solution

16% solution is 100%

Ok here goes my first gmat club post! After spending a good 6 mins on this problem I can provide some good insight

So the total is 10 kg. We are told to remove from the mixture and replace with pure sand. This means that the total is still 10 kg.

Now, let X be the amount of pure sand that is added. This is what we are solving for.

Now the sand in the mixture is going to be (10-X)*0.3 + X. The first part is the sand that is in the mixture now WITHOUT the addition of the additional sand. To make this more clear, (10-X) is the amount of sand and clay mixture with the subtraction of the pure sand that will be added. Multiplying it by 0.3 gives us the amount of sand in this part of the whole mixture. the second part is the additional amount of pure sand that is added. Note that we do not multiply this by any percent number because it is pure sand!

So now the whole equation will look like this:

(10-X)*0.3+X/((10-X)+X) = 0.5.

The numerator is the amount of sand in the mixture. (10-X)*0.3 = amount of sand that is not pure in the mixture. X is the amount of pure sand.

(10-X)*0.3 + X = 5.
3-0.3X+X = 5.
0.7X = 2.
X = 20/7.

Here is another method:

Consider that solution is made of sugar and water:
Solution A: Total 1000gm (10% sugar)
1000= 900 (water) + 100 (Sugar)

Expected Solutin B: Total 1000gm (16% sugar)
1000= 840 (water) + 160 (Sugar)

Now, as said in the question 25% of the solution A is replaced with another solution, which means:
75% of the solution A in untouched and only 25% of the solution (250gm) is touched

Total Sugar in Solution B= 160 = (75% of sugar in solution A) + (sugar replaced in 25% of Solution A with a new solution)

Sugar replaced in 25% Solution A with a new solution = 160- 75 =85

Sugar in new solution: 85/250 = 340/1000 = 34% (Answer)

Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.

3 parts of 10% + 1 part of x (unknown) % = 4 parts of 16%
=> x% = 64%-30% = 34%

ans A it is.

Alligation is the KEY

3/4 of 10%------------------------------1/4 of X%

-------------------16%----------------------------


(X-16)%------------------------------------------6%

(X-16)/6=3/1

X=34%

This is called Alligation or the scale method (a variant). Read more about this method here: http://www.veritasprep.com/blog/2011/03 ... -averages/
_________________

Total Solution ........................ Sugar Concentration

100 ............................................ 10
(Assumed)

25% solution removed

100-25 ......................................... \(10-\frac{10}{4}\)


75 ................................................... \(\frac{30}{4}\)

Same quantity has been replaced. Say the new solution sugar weight = x%

75 + 25 ......................................... \(\frac{30}{4} + \frac{25x}{100}\)

Given that the resultant solution has sugar concentration of 16%

So equating the above

\(\frac{30}{4} + \frac{25x}{100} = 16\)

x = 34%

Answer = A

Great! Keep practicing!
_________________