In a Chemistry lab, there are three solutions of an acid A, B and C

Question

In a Chemistry lab, there are three solutions of an acid – A, B and C – of concentrations 45%, 50% and c% respectively. If 100 ml of A when mixed with V ml of C, produces a solution of 60% concentration and 100 ml of B when mixed with V ml of C, produces a solution of 62% concentration, what is the value of V?

A. 80
B. 100
C. 120
D. 150
E. 175

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RenukaKhope · Answer

The value for v is 150 ml?

Souradeep17 · Answer

Solution A+ solution C
We can write it as 
45% of 100 + C% of V= 60% (100+v)

45+.CV=60+.60V
15=.CV-.06V..eq 1

Solution B+C
50% of 100+c% of V=62% (100+V)
50+.CV=62+.62V
12=.CV-.62V..eq 2

Equating CV from both eq

15=.60V=12+.62V
3=.02V
V=150 (option D)

okHedwig · Answer

Is there any short method to solve this apart from using substitution?

egmat · Answer

okHedwig

Yes, there's a powerful shortcut using the "Weighted Average Difference" technique!

Here's the clever approach that avoids substitution entirely:

Key Insight: 
When the same volumes are mixed ( 100  ml and  V  ml in both cases), the difference in final concentrations tells us about the relationship between solutions.

The Shortcut Method:

Step 1: Set up the concentration differences 
- Mixture 1:  100  ml of  45\%  +  V  ml of  c\%  =  60\% 
- Mixture 2:  100  ml of  50\%  +  V  ml of  c\%  =  62\%

Step 2: Find the impact of changing from A to B 
When we switch from solution A ( 45\% ) to solution B ( 50\% ):
- The  100  ml portion increases by  5\%  (from  45\%  to  50\% )
- The final concentration increases by  2\%  (from  60\%  to  62\% )

Step 3: Calculate the volume ratio 
The  5\%  increase in  100  ml causes a  2\%  increase in the total mixture.
This means:  \frac{100}{100 + V} = \frac{2}{5}

Solving:  500 = 200 + 2V 
Therefore:  V = 150

Why This Works: 
The weighted average principle tells us that the impact of changing one component is proportional to its weight in the mixture. When  100  ml represents  \frac{2}{5}  of the total mixture, we can directly calculate  V .

Time-Saving Tip for GMAT: 
Whenever you see two mixtures with:
- Same volumes being mixed
- Different concentrations of one component
- Different final results

Think "weighted average difference" instead of setting up two equations!

Practice Recognition Pattern: 
Look for problems where:
 
 Two similar mixtures are created 
 Only one component changes between them 
 You need to find the unknown volume or concentration

This technique can save you 1-2 minutes on similar GMAT problems - time you can use elsewhere!

You can practice similar mixture and weighted average problems   here   - focus on concentration and ratio questions to master these shortcut techniques. This   free trial   covers systematic approaches to time-saving methods and pattern recognition for various Quant concepts.

In a Chemistry lab, there are three solutions of an acid A, B and C

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In a Chemistry lab, there are three solutions of an acid A, B and C

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