Ratio and Proportion

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MoniMini

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Nov 4, 2011
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Hello,
This is my first time here so I am a bit lost and can't get the right place to post a problem based on Ratio Proportion. May I please know which category will sums related to this topic be posted to?
Any help will be appreciated.

Getting back to Maths,
I have got stuck on this Ratio and Proportion problem in an Olympiad Practice Book.
Can you kindly tell me what will be the solution?

The question is-

A mixture contains alchohol and water in the ratio 4 : 3. If 7 litres of water is added to the mixture, the ratio of alchohol to water becomes 3 : 4. Find the quantity of alchohol in the mixture.

a) 12 Litres b) 13 Litres c) 14 Litres d) 15 Litres

Thank You,
~MoniMini;)
 
MoniMini said:
Hello,
This is my first time here so I am a bit lost and can't get the right place to post a problem based on Ratio Proportion. May I please know which category will sums related to this topic be posted to?
Any help will be appreciated.

Getting back to Maths,
I have got stuck on this Ratio and Proportion problem in an Olympiad Practice Book.
Can you kindly tell me what will be the solution?

The question is-

A mixture contains alchohol and water in the ratio 4 : 3. If 7 litres of water is added to the mixture, the ratio of alchohol to water becomes 3 : 4. Find the quantity of alchohol in the mixture.

a) 12 Litres b) 13 Litres c) 14 Litres d) 15 Litres

Thank You,
~MoniMini;)
Click to expand...

A/W = 4/3

A/(W+7)=3/4

what is A?
 
Hello, MoniMini!

Welcome aboard!
A slightly different approach . . .


A mixture contains alcohol and water in the ratio 4:3.
If 7 liters of water is added to the mixture, the ratio of alcohol to water becomes 3:4.
Find the quantity of alcohol in the mixture.

. . (a) 12 liters . . (b) 13 liters . . (c) 14 liters . . (d) 15 liters
Click to expand...

We have: .\(\displaystyle \begin{Bmatrix} \dfrac{A}{W} &=& \dfrac{4}{3} & [1] \\ \\ \dfrac{A}{W+7} &=& \dfrac{3}{4} & [2] \end{Bmatrix}\)

Solve the system of equations . . .


From [1], we have: .\(\displaystyle W \:=\:\frac{3}{4}A\;\;[3]\)

From [2], we have: .\(\displaystyle 4A \:=\:3W+21\;\;[4]\)


Substitute [3] into [4]: .\(\displaystyle 4A \:=\:3\left(\frac{3}{4}A\right) + 21\)

. . \(\displaystyle 4A \:=\: \frac{9}{4}A + 21 \quad\Rightarrow\quad \frac{7}{4}A \:=\:21 \quad\Rightarrow\quad A \:=\:12\) .(a)
 
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