Question

Beaker A consists of sugar and water mixture in ratio 5:3 and beaker B has the same mixture in ratio 2:3. These two mixtures are mixed to form a new mixture containing half sugar and half water.
In what ratio they must be taken?

Answer 1

Assuming both beakers A and B are of the same volume,
We can simply add the ratios of sugar to water appropriately as shown below to get the mixture's ratio if all of A is mixed with B.
((5/8)+(2/5)):((3/5)+(3/8))
This gives us
41:39.
Therefore A and B can't be mixed in 1:1 ratio. So to find this ratio we can introduce an unknown variable 'x' to the mixture's ratio ie.,
(((5/8)*x)+(2/5)):(((3/8)*x)+(3/5))
And since the the final mixture's sugar to water ratio is 1:1

(((5/8)*x)+(2/5))=(((3/8)*x)+(3/5))
x= 4/5
Which means (4/9) of A must be mixed with (5/9) of B for the final mixture to have sugar to water ratio as 1:1.

Answer 2

Let X = quantity taken by beaker A
Let Y = quantity taken by beaker B
Then we can write the equation
X x 5/8 + Y x 2/5 = X x 3/ 8 + Y x 3/ 5
Rearranging the equation, it yields : X / Y = 8/10
The answer is 8 parts of A and 10 parts of B

Comments

What do you mean by 8 parts of A? (1/8)th of A ? 8/18 of A ?

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What is the percentage of A and B are you suggesting for your answer ?

Answer 3

Answer 444.444:555.556

Excuse my poor English. I can't explain sufficiently.
In the mixture of beaker A, there is 62.5% of sugar. And in beaker B there is 40% of sugar.

If the new mixture containing half sugar and half water is 1000g, the mixture of beaker A is 444.444g and the mixture of beaker B is 555.556g. (62.5x+40y=500, x+y=1000 ⇒ x=444.444, y=888.889 < in 1000g of new mixture there is 500g of sugar>)
If the new mixture containing half sugar and half water is 2000g, the mixture of beaker A is 888.889g and the mixture of beaker B is 1111.111g.

Answer 4

Answer is 0ne to two:

1 ( 5 w + 3 s ) + 2 ( 2 w + 3 s ) = 9 w + 9 s

Comments

This was my solution but it is wrong! I apologize !! the answer 4/5 is correct.