Questions & Answers

Question

Answers

A.60gm

B.90gm

C.120gm

D.150gm

Answer
Verified

Hint: The given problem is related to the concept of percentage. First, find the initial amount of sugar in the solution. Then, consider the added amount as x gm. Form equation in x by using the information from the question.

Complete step by step answer:

First, we will find the initial amount of sugar in the sugar solution It is given that 600 gm of sugar solution has 40% sugar in it. So, the initial amount of sugar is 40% of 600 gm, which can be calculated as $40%\times 600=\dfrac{40}{100}\times 600$ = 240 gm. Now, let the amount added be x gm. On adding x gm of sugar in the solution, the weight of sugar will increase by x gm, and the weight of the solution will also increase by x gm. So, the new weight of sugar = (240 + x) gm, and the new weight of the sugar solution = (600 + x) gm. Now, it is given that the amount of sugar in the solution is 50%. So, $\dfrac{240+x}{600+x}=\dfrac{50}{100}$ . On cross multiplication, we get $240+x=50\times \left( 600+x \right)$ .

$\Rightarrow 24000+100x=30000+50x$

$\Rightarrow 50x=6000$

\[\Rightarrow x=\dfrac{6000}{50}=120\]

So, the amount of sugar added in the solution is 120 gm.

Note: While forming equations, and while doing calculations, be careful of sign convention. Sign mistakes are very common and can lead to wrong answers. So, they should be avoided. Also, be careful of the units. If the unit of an entity is taken as gram in one case, then it should be taken as gram everywhere. This will avoid confusion and will make the solution easier.

Complete step by step answer:

First, we will find the initial amount of sugar in the sugar solution It is given that 600 gm of sugar solution has 40% sugar in it. So, the initial amount of sugar is 40% of 600 gm, which can be calculated as $40%\times 600=\dfrac{40}{100}\times 600$ = 240 gm. Now, let the amount added be x gm. On adding x gm of sugar in the solution, the weight of sugar will increase by x gm, and the weight of the solution will also increase by x gm. So, the new weight of sugar = (240 + x) gm, and the new weight of the sugar solution = (600 + x) gm. Now, it is given that the amount of sugar in the solution is 50%. So, $\dfrac{240+x}{600+x}=\dfrac{50}{100}$ . On cross multiplication, we get $240+x=50\times \left( 600+x \right)$ .

$\Rightarrow 24000+100x=30000+50x$

$\Rightarrow 50x=6000$

\[\Rightarrow x=\dfrac{6000}{50}=120\]

So, the amount of sugar added in the solution is 120 gm.

Note: While forming equations, and while doing calculations, be careful of sign convention. Sign mistakes are very common and can lead to wrong answers. So, they should be avoided. Also, be careful of the units. If the unit of an entity is taken as gram in one case, then it should be taken as gram everywhere. This will avoid confusion and will make the solution easier.

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