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:

Let the required ratio be x:y

Liquid A in x litres of mixture in container 1 =

6

5x

litres

Liquid B in x litres of mixture in container 1 =

6

x

litres

Liquid A in y litres of mixture in container 2 =

4

y

litres

Liquid B in y litres of mixture in container 2 =

4

3y

litres

∴ Liquid A: Liquid B = [

6

5x

+

4

y

]:[

6

x

+

4

3y

]

Given,

6

x

+

4

3y

6

5x

+

4

y

=

1

1

⇒

6

5x

+

4

y

=

6

x

+

4

3y

⇒

6

5x

−

6

x

=

4

3y

−

4

y

⇒

6

4x

=

4

2y

⇒

3

2x

=

2

y

⇒

y

x

=

4

3

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