Question

Two liquids A and B are in the ratio 5 : 1 in cotainer and 1 : 3 in container 2. In what ratio should the contents be mixed so as to obtain a mixture of A and B in the ratio 1 : 1 ?​

Answer 1

Answer:

Container 1:

Let each part be x.

Vol of A= 5x ; Vol of B= x ; Total Vol= 6x.

Container 2:

Let each part be y.

Vol of A= y ; Vol of B= 3y; Total Vol= 4y.

After Mixing:

Vol of A= 5x + y

Vol of B= x + 3y

As Ratio of A:B is 1:1, hence

5x+y = x+3y

2x = y

So,

Ratio of Total Vol 1 : Total Vol 2 =

6x / 4y = 6x / 4(2x) = 6/8 = 3/4

Step-by-step explanation:

Answer 2

Answer:

$\huge\underline\bold {Answer:}$

Let the required be x : y

Liquid A in x litres of mixture in container 1

= 5x/6 litres

Liquid B in x litres of mixture in container 1

= x/6 litres

Liquid A in y litres of mixture in container 2

= y/4 litres

Liquid B in y litres of mixture in container 2

= 3y/4 litres

Therefore Liquid A : Liquid B

$= ( \frac{5x}{6} + \frac{y}{4} ) \div ( \frac{x}{6} + \frac{3y}{4} )$

Given,

$\frac{( \frac{5x}{6} + \frac{y}{4} ) }{( \frac{x}{6} + \frac{3y}{4} )} = \frac{1}{1}$

=> 5x/6 + y/4 = x/6 + 3y/4

=> 5x - x/6 = 3y/4 - y/4

=> 4x/6 = 2y/4

=> 2x/3 = y/2

=> x/y = 3/4.

Therefore in 3/4 ratio the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1