Question

A cask contains 12 gallons of mixture of wine and water in ratio 3:1.How much of the mixture must be drawn off and water substituted , so that the wine and water in the cask may become half and half.

Answer 1

a. 3 litres
b. 5 litres
c. 7 litres
d. none of these

Answer 2

4 litres ?

Answer 3

yes it is 4 litres

Answer 4

have u figured out any method

Answer 5

since cask capacity is 12L, we want to have 6L wine and 6L water
right now the cask has 9L wine and 3L water (3 : 1 ratio)

Answer 6

that means we need to remove 3L wine
which is same as removing 4L mixture

Answer 7

how can half-half does necessarily mean 6L and 6L

it could also be 3L(wine) and 3L(water), 4L(wine) and 4L(water), etc

Answer 8

we're given 12L of mixture to start with, right ?

Answer 9

yes

Answer 10

and we're told that the removed mixture must be substituted with water

so water + wine in the cask must add up to 12L

Answer 11

yes

Answer 12

oh lol

Answer 13

but i always try to look for equation to solve them

Answer 14

i feel equations can complicate matters here

Answer 15

it would be like killing a rat with an atom bomb

Answer 16

(jk)

Answer 17

haha

Answer 18

ok that makes sense ,then m kind of a silly

Answer 19

whats your method for solving this ?

Answer 20

this a question from ratio and proportion , i couldn't solve that, i dont know how to form equations (ratio)in this situation

Answer 21

suppose we need to remove \(x\) L from the mixture, then we will be removing \(\dfrac{3}{4}x\) L of wine, yes ?

Answer 22

after removing \(x\)L mixture, we want the amount of wine in the cask to be \(6\)L, so :

\[9 - \frac{3}{4}x = 6\]

solve \(x\)