How many liters of a solution that is 15 percent salt must be added to

Question

How many liters of a solution that is 15 percent salt must be added to 5 liters of a solution that is 8 percent salt so that the resulting solution is 10 percent salt?

A. 1
B. 1.5
C. 2
D. 2.5
E. 3

BrentGMATPrepNow · Accepted Answer

When solving mixture questions, it can be useful to sketch the solutions with the ingredients SEPARATED. 
8% of 5 liters = 0.4 liters. So, the original mixture contains   0.4   liters of salt

Let x = the volume (in liters) of 15% solution required
So, this solution contains   0.15x   liters of salt

We get:
 https://i.imgur.com/Wz56TjT.png

We want the resulting solution to be 10% salt.

In other words, we want:  \frac{0.4 + 0.15x}{5+x}=\frac{10}{100}  (aka 10%)

Simplify:  \frac{0.4 + 0.15x}{5+x}=\frac{1}{10}

Cross multiply:  (10)(0.4 + 0.15x) = 5+x

Expand:  4 + 1.5x = 5+x

Solve:  x = 2

Answer: C

Cheers,
Brent

sujoykrdatta · Answer

The basic rule for any average is that if you add the deviations about the mean for all the numbers, the result is ZERO
In this question, the average of x units of 15% salt and 5 units of 8% salt is 10% salt
The deviations are: 
# 15% - 10% = 5% taken x times = 5x
# 8% - 10% = -2% taken 5 times = -10

Since the sum of deviations must be ZERO, we have:

5x - 10 = 0 
=> x = 2

Answer C

CrackverbalGMAT · Answer

CONCEPT: Alligation technique in mixtures

SOLUTION: Let there be x Lit of 15% salt conc.
Using Alligation,
Absolute Concentration of 8% solution/Absolute Conc. of 15% solution = 15-10/10-8
=>5/x=5/2=>x=2 (C)

Hope this helps

Devmitra Sen

Attachments

20201202_182025-01.jpeg [ 2.41 MiB | Viewed 18529 times ]

Devmitra Sen

yashikaaggarwal · Answer

Let the solution with 8% salt be A
and the solution with 15% salt be B
so,
8A/100 + 15B/100 = (A+B)10/100
8A+15B = 10A+10B
5B = 2A
Where A = 5
5B = 10
B = 2

Answer is C

Varane · Answer

Can you please share your approach for these types of questions  avigutman

Posted from my mobile device

avigutman · Answer

We're looking at an average of ratios here, Varane . 10% is going to be the average of 8% and 15% if the ratio of the quantities is 5:2. Here's a playlist full of video solutions from which you can learn how to make the inference that I just made: https://youtube.com/playlist?list=PLWmy ... Ne2QMlbgAu

vv65 · Answer

5 litres of the base solution has 400 grams salt
1 litre of the 15% solution has 150 grams of salt

Start with checking answer choice C:
(because it's in the middle) 
We add 2 litres of the 15% solution to 5 litres of the base
The 2 litres have 300grams of salt
The result is 7 litres of solution with 700 grams salt

That is a 10% solution, and C is the answer

Posted from my mobile device

Phoenix19 · Answer

Step 1 let 15% soln be x ltrs
Step 2 Total Weight of soln = x + 5 ltrs
Step 3 Now equation looks like (x +5) 10/100 = 5 * (8/100 )+ x*(15/100). On solving x = 2

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

How many liters of a solution that is 15 percent salt must be added to

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

How many liters of a solution that is 15 percent salt must be added to

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards