Question

Find the ratio in which the contents of 2 jars A & B containing spirit & water in the ratio 1:3 & 3:2 respectively must be mixed so that resulting mixture contains 45% spirit?​

Answer 1

$\bf\small\red{Given:-}$

$\sf\rightarrow spirit \: in \: 1 litres \: mix \: of \: X \: = \frac{5}{7} litres.$

$\sf\rightarrow \: spirit \: in \: 1 litres \: mix \: Y = \frac{7}{13} litres.$

$\sf\rightarrow \: spirit \: in \: 1 \: litres \: mix \: Z = litres.$

$\bf\small\red{Find :-}$

$\sf\rightarrow \: required \: ratio \: of \: a :\: b$

$\bf\small\red{Solution:-}$

By rule of allegations,we have to find A:B ratio.

A : B

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{ 8}{13}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{13} : \: \: \: \: \frac{9}{19}$

$\sf\dashrightarrow \: so \: answer \: is \: = \frac{1}{13} :\frac{9}{19}$

Answer 2

Given  : 2 jars A & B containing spirit & water in the ratio 1:3 & 3:2 respectively  

To Find :  ratio in which   must be mixed  resulting mixture contains 45% spirit  

Solution:

Let say its mixed in  4x : 5y ratio

Jar  A    4x   litre  and Jar B   5y  litre

Jar A  spirit & water in the ratio 1:3  

=> Sprit  = x   and water  =  3x

Jar B  spirit & water in the ratio  3 : 2

=> Sprit  = 3y   and water  =  2y

Total spirit =    x + 3y

Total water  =  3x  + 2y

Total mixture  =  4x  + 5y

resulting mixture contains 45% spirit

=> x  + 3y  = (45/100) (4x + 5y)

=> x  + 3y  = (9/20) (4x + 5y)

=> 20x  + 60y  = 36x  + 45y

=> 15y = 16x

=>  y  = 16x /15

mixed in  4x : 5y ratio

=  4x  :  5( 16x /15)

=  4  :   16 / 3

= 12 : 16

=  3  :  4

must be mixed  in  3 : 4  ratio

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