Problem Solving

A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

OA is B
What could be the correct answer to this? An Expert contribution will be appreciated.

A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

OA is B
What could be the correct answer to this? An Expert contribution will be appreciated.

Hi Roland2rule,
Let's take a look at your question.

7.5 litre mixture of water and sugar is 60% sugar.
Amount of sugar in 7.5 litre mixture is:
$$=7.5\times\frac{60}{100}$$
$$=\frac{75}{10}\times\frac{3}{5}$$
$$=\frac{15}{10}\times3$$
$$=\frac{45}{10}=4.5$$

It means, in 7.5 Litres of mixture of water and sugar, 4.5 litres is sugar and remaining 3 litres is water.
When 1.5 litres of water is added to the mixture,
Total amount of water in mixture = 3 + 1.5 = 4.5 litres.

Now the mixture has 4.5 litres of sugar and 4.5 litres of water.
Equal amount means that the mixture contains 50% sugar and 50% water.

Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

Roland2rule wrote:A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

Alternate approach:

Since (added water)/(original volume) = (1.5)/(7.5) = 15/75 = 1/5, the total volume increases by 1/5.
Put another way, the resulting volume is 6/5 of the original volume.
As a result, the sugar percentage is multiplied by the RECIPROCAL of the fraction in red:
(60%)(5/6) = 50%.

The correct answer is B.

Another example:

A 100-liter mixture of water and sugar is 40% sugar. If 60 liters of water is added, approximately what is the % of the new mixture of sugar?

Since (added water)/(original volume) = 60/100 = 3/5, the total volume increases by 3/5.
Put another way, the resulting volume is 8/5 of the original volume.
As a result, the sugar percentage is multiplied by the RECIPROCAL of the fraction in red:
(40%)(5/8) = [spoiler]25%[/spoiler].