Question

# 600gm of Sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?A.60gmB.90gmC.120gmD.150gm

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 $240+x=50\times \left( 600+x \right)$ .
$\Rightarrow 24000+100x=30000+50x$
$\Rightarrow 50x=6000$
$\Rightarrow x=\dfrac{6000}{50}=120$