Question

420 grams of sugar solution has 40% sugar in it. How much more sugar needs to be added (in grams), such that the resulting solution has 65% sugar? also explain

Answer 1

Given:

420 grams of sugar solution has 40% sugar in it.

To find:

How much more sugar needs to be added (in grams), such that the resulting solution has 65% sugar?

Solution:

The total weight of sugar solution = 420 g

The percentage of sugar in the solution = 40%

∴ The weight of sugar in the solution = $\frac{40}{100} \times 420 = 168 \:g$

Let "x" represent the required amount of sugar that needs to be added.

After adding "x" g of sugar,

The new weight of sugar = (168 + x) g

The new weight of the sugar solution = (420 + x) g

The percentage of sugar in the new mixture = 65%

Therefore, we can form an equation as:

$\frac{168\:+\:x}{420\:+\:x}\times 100 = 65$

$\implies (168\:+\:x)100 = (420\:+\:x)65$

$\implies 16800 + 100x = 27300 + 65x$

$\implies 100x - 65x = 27300 - 16800$

$\implies 35x = 10500$

$\implies x = \frac{10500}{35}$

$\implies \bold{x = 300}$

Thus, 300 g more sugar needs to be added such that the resulting solution has 65% sugar.

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