Find the ratio in which the contains 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?
Answers
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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Answer: So mixture contains 45% spirit..
Step-by-step explanation: If 45% is spirit then water will be 55%.
Take it as a ratio
45% : 55%
% will get cancelled
Ratio become 9:11
Now just use alligation
1:3 3:2
9:11
3 : 2