Question

Kiran creating an alcohol solution by mixing two different alcohol solutions of 15% and 20% respectively. If the resulting mixture has 18% alcohol content, what is the ratio of the volume of alcohol solutions used?
1. 1 : 3
2.  2 : 3
3. 5 : 2
4. 2 : 1

Answer 1

Correct Answer - Option 2 :  2 : 3

Calculation:

Let volume of alcohol solutions are V₁ and  V₂ respectively.

⇒ Volume of alcohol in the resulting mixture = 15% of V₁ + 20% of V₂

⇒ ((15/100) × V₁) + ((20/100) × V₂)

⇒ (15V₁+ 20V₂ )/100

which is also equal to 18% of (V₁ + V₂).

⇒ (15V1+ 20V2 )/100 = (18 × (V1 + V2))/100

⇒ 2V₂ = 3V₁

The ratio of volume is 2 : 3 .

If a mixture of Q1 quantity C1% content is mixing with Q2 quantity C2% mixture, and the concentration of the new mixture is Cnew% , then the following equation can be used

C1% of Q1 + C2% of Q2 = Cnew% of (Q1 + Q2)

⇒ C1Q1 + C2Q2 = Cnew(Q1 + Q2)