Question

Question 146(iv)
The table shows the portion of some common materials that are recycled.
$\begin{array}{cc}\text{Material}& \text{Recycled}\\ \text{Paper}& \frac{5}{11}\\ \text{Aluminium cans}& \frac{5}{8}\\ \text{Glass}& \frac{2}{5}\\ \text{Scrap}& \frac{3}{4}\end{array}$
Arrange the rate of recycling the materials from the greatest to the smallest.

Answer 1

Taking LCM of 11, 8, 5, 4 = 440

Now, portion of paper recycled
$=\frac{5}{11}=\frac{5}{11}\times \frac{40}{40}=\frac{200}{440}$

portion of aluminium cans recycled
$=\frac{5}{8}=\frac{5}{8}\times \frac{55}{55}=\frac{275}{440}$

portion of glass recycled
$=\frac{2}{5}=\frac{2}{5}\times \frac{88}{88}=\frac{176}{440}$

portion of scrap recycled
$=\frac{3}{4}=\frac{3}{4}\times \frac{110}{110}=\frac{330}{440}$

As, $\frac{330}{440}>\frac{275}{440}>\frac{200}{440}>\frac{176}{440}$

i.e. $\frac{3}{4}>\frac{5}{8}>\frac{5}{11}>\frac{2}{5}$

That means, Rate of recycling of materials is :
Scrap > Aluminium cans > Paper > Glass.