Question

A jar full of whisky contains 40% of alcohol. A part of whisky is replaced by another containing 19% of alcohol and now new alcohol be 26%, find the quantity of whisky replaced.

Answer 1

Solution:

Amount of Alcohol in jar which contains full of whisky =40%

So,Amount of water = 100-40=60%

It is also, given that a part of whisky is replaced by another containing 19% of alcohol and now new alcohol be 26%.

The Whisky which has replaced the Whisky in the Jar

Amount of Alcohol =19%

Amount of Water =100-19=81%

In new Whisky

Amount of Alcohol =26 %

Amount of Water = 100 -26=74%

Writing in terms of equation with the help of variable ,x and y

40%x +19%y=26%

60% x + 81%y=74%

1.40 x +19 y=26-----×3

2.60 x + 81 y= 74-------×2

1.→120 x + 57 y = 78

2.→120 x + 162 y = 148

(1) - (2)

-105 y = -70

$y=\frac{70}{105}\\\\{\text{Dividing numerator and denominator by 35}}\\\\=\frac{2}{3}$

Substituting value of ,y in equation (2)

$60 x +81 \times \frac{2}{3}=74\\\\ 60 x+54=74\\\\60 x=74-54\\\\60 x=20\\\\x=\frac{20}{60}\\\\x=\frac{1}{3}$

So, in the beginning Amount of Whisky that is amount of water in the jar =60%

Amount of Alcohol in the beginning in the Jar =40%

Amount of Whisky Replaced

 $=60 \times \frac{2}{3}+40 \times \frac{1}{3}\\\\=40+\frac{40}{3}\\\\=\frac{160}{3}$

Amount of alcohol in the Whisky

     $=\frac{\frac{40}{3}}{\frac{160}{3}}\times 100\\\\=\frac{40}{160}\times 100=25$%

Amount of water in the Whisky

     $=\frac{\frac{40}{1}}{\frac{160}{3}}\times 100\\\\=\frac{120}{160}\times 100=75$%

Answer 2

Answer:

2/3 of whisky is replaced

Step-by-step explanation:

Let say Jar Volume = 100 V ml

ALCOHOL= 40V

Non-Alcohol = 60V

Let say X  ml is replaced

so Reduced Alcohol  = 0.4X

Reduced non alcohol =  0.6X

Added Alcohol = 0.19X

Added non-alcohol = 0.81X

New Alcohol = 40V - 0.4X + 0.19X = 40V - 0.21X

New non-alcohol = 60V - 0.6X + 0.81X = 60V + 0.21X

New Alcohol % = (40V - 0.21X)/100V * 100

(40V - 0.21X)/100V * 100 = 26

=> 40V - 0.21X = 26V

=> 14V = 0.21X

=> X = 14V/(0.21)

=> X = 200V/3

=> X = (2/3) 100V

2/3 of whisky is replaced