Question

Question 67

Three bags contain 64.2 kg of sugar. The second bag contains $\frac{4}{5}$ of the contents of the first and the third contains $45\frac{1}{2}\%$ of what there is in the second bag. How much sugar is there in each bag?

Answer 1

The total weight of sugar in three bags = 64.2 kg
Let the first bag contains x kg sugar.
The second bag contains $=x\times \frac{4}{5}kg=\frac{4x}{5}kg$
Third bag contains = $=x\times \frac{4}{5}\times \frac{91}{2}\%=x\times \frac{4}{5}\times \frac{\frac{91}{2}}{100}=\frac{91x}{250}kg$
According to the question,
$x+\frac{4x}{5}+\frac{91x}{250}=64.2\Rightarrow \frac{250x+200x+91x}{250}=64.2\Rightarrow 541x=64.2\times 250$
541x = 16050
$\Rightarrow x=\frac{16050}{541}=29.67kg$
So, first bag contains the sugar = 29.67 kg
Second bag contains the sugar = $29.67\times \frac{4}{5}=23.73kg$
and third bag contains the sugar $=\frac{91}{250}\times 29.67=10.8kg$