Question

in a mixture , the ratio of the alcohol and water is 6:5 . when 22 liter mixture are replaced by water , the ratio become 9:13 , find the quantity of water after replacment​

Answer 1

Answer:

52 liters

Step-by-step explanation:

According to the question,

6x – 22 × 6/11 : 5x – 22 × 5/11+ 22 = 9 : 13

6x – 12 : 5x – 10 + 22 = 9 : 13

13 (6x – 12) = 9 (5x + 12)

78x – 156 = 45x + 108

78x – 45x = 156 + 108

33x = 264

x = 8

Water after replacement = 5 × 8 – 10 + 22 = 40 + 22 = 52 litre

Answer 2

Answer:

Since we have given that

Ratio of alcohol to water = 6:5

Quantity of mixture = 22 liters

So, the capacity of alcohol = \dfrac{6}{11}\times 22=6\times 2=12

11

6

×22=6×2=12

the capacity of water = \dfrac{5}{11}\times 22=5\times 2=10\ liters

11

5

×22=5×2=10 liters

According to question, we get that

\begin{gathered}\dfrac{6x-12}{5x-10+22}=\dfrac{9}{13}\\\\\dfrac{6x-12}{5x+12}=\dfrac{9}{13}\\\\13(6x-12)=9(5x+12)\\\\78x-156=45x+108\\\\78x-45x=108+156\\\\33x=264\\\\x=\dfrac{264}{33}=8\end{gathered}

5x−10+22

6x−12

=

13

9

5x+12

6x−12

=

13

9

13(6x−12)=9(5x+12)

78x−156=45x+108

78x−45x=108+156

33x=264

x=

33

264

=8

So, the water would be

5x+12=5(8)+12=40+12=52\ liters5x+12=5(8)+12=40+12=52 liters

Hence, there is 52 liters of water after replacement.

# learn more:

Illustration 18: A mixture contains alcohol and water

in the ratio of 6:1. On adding 8 litres of water, the ratio

of alcohol to water becomes 6:5. Find the quantity of

water in the mixture.