Question

The ratio of sprit and water is 2 : 5. If the volume of solution is increased by 50% by adding sprit only. What is the resultant ratio of sprit and water?

• A. 9 : 10
• B. 12 : 15
• C. 11 : 10
• D. 3 : 4

Answer 1

Answer:

C. 11 : 10

Solution:

Given:

The ratio of sprit and water = 2 : 5

Formula used:

If the volume is increased by a%, then the new volume will be $[\frac{(100 + a)}{100}]\times{Initial volume}$

Calculation:

Let an amount of sprit and water be 2 x and 5 x respectively and also let y liter is added to sprit.

Total volume = 2 x + 5 x

⇒ Total volume = 7 x

After adding y liter, new volume = 7 x + y

According to the question, the new volume of a solution is increased by 50% after adding sprit only.

⇒ The new volume of a solution $=[\frac{(100 + 50)}{100}]\times{7x}$

⇒ $7x+y=[\frac{150}{100}]\times{7x}$

⇒ 7 x + y = 10.5 x 

⇒ 10.5 x – 7 x = y

⇒ 3.5 x = y

⇒ $\frac{x}{y} = \frac{1}{3.5}$

 

The resultant ratio of sprit and water $=\frac{(2x+y)}{5x}$

⇒ The resultant ratio of sprit and water $= (\frac{2x}{5x})+\frac{y}{5x}$

⇒ The resultant ratio of sprit and water $= \frac{2}{5}+\frac{3.5}{5}$

⇒ The resultant ratio of sprit and water $= \frac{(2 + 3.5)}{5}$

⇒ The resultant ratio of sprit and water $= \frac{5.5}{5}$

⇒ The resultant ratio of sprit and water $= \frac{11}{10}$

∴ The resultant ratio of sprit and water is $\frac{11}{10}$

Alternate Method 

Ratio of sprit and water = 2 : 5

Let the Sprit and water be 20x and 50x respectively.

Initial total volume = (20x + 50x) = 70x

Then, the volume of solution increased by 50% means,

⇒ $(70x)\times${50%}= 35x

⇒ 70x + 35x = 105x

According to the question, 

Only sprit is added in the solution and water is same as before.

New total volume = 105x 

New sprit solution = new total volume - initial water solution

⇒ new sprit solution = 105x - 50x = 55x

Resultant ratio of sprit and water = 55x : 50x

⇒ Ratio = 11 : 10

∴ The resultant ratio of sprit and water is 11 : 10