Question

The ratios of acid and water in vessels A and B are 4 : 5 and 7 : 5, respectively. In what ratio should the contents of A and B be mixed to get a solution containing 50% acid?

• A. 4 : 3
• B. 2 : 3
• C. 3 : 2
• D. 3 : 4

Answer 1

Answer:

C. 3 : 2

Solution:

Given :

The ratios of acid and water in vessels A and B are 4 : 5 and 7 : 5, respectively.

Calculations :

The ratio of acid to water in vessel A is 4 : 5 

Let the total volume of acid and water be 4x and 5x 

The ratio of acid to water in vessel B is 7 : 5 

Let the total volume of acid and water be 7y and 5y

According to the question volume of water and acid must be equal 

So,

(4x + 7y) : (5x + 5y) = 1 : 1 

⇒ x = 2y 

Putv value of x = 2y to get volume 

Volume of vessel A = 4x + 5x = 9x 

⇒ 18y 

Volume of vessel B = 7y + 5y 

⇒ 12y 

Ratio of vessel A to B 

Volume of vessel A : Volume of vessel B = 18y : 12y 

⇒ 3 : 2 

∴ 3 : 2 will be the ratio at which vessel A and B must be mixed  

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