A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is -
A. 3 litres
B. 4 litres
C. 15 litres
D. 10 litres
Answer: Option D
Solution (By Examveda Team)
Let the quantity of alcohol and water be 4x litres and 3x litres respectively$$\eqalign{ & \frac{{4x}}{{\left( {3x + 5} \right)}} = \frac{4}{5} \cr & \Rightarrow 20x = 4\left( {3x + 5} \right) \cr & \Rightarrow 8x = 20 \cr & \Rightarrow x = 2.5 \cr} $$
Quantity of alcohol
= (4 × 2.5) litres
= 10 litres.
This Question Belongs to Arithmetic Ability >> Alligation
This is how it is:
Quantity of water in both cases: 3x/7 and 5x/9
take water quantity equal:
3x/7 + 5 = 5/9 (x+5)
x = 17.5
Alcohol quantity: 4x/7 = 10
Although the answer is right but solution is illogical. How can you assume the quantity of water from a ratio like that.
extracting water quantity from ratio would be: 4/7x and 4/9x
then solve it by taking quantity of water in both cases equal and you will find the answer.