Question

Campus and Welfare Committee of the school is planning to develop a blue shade for painting the entire school building. For this purpose various shades are tried by mixing containers of blue paint and white paint. In each of the following mixtures, decide which is a lighter shade of blue and also find the lightest blue shade among all of them.


If one container has one liter paint and the building requires $105$ liters for painting, how many containers of each type are required to paint the building in the lightest blue shade?

Answer 1

Calculating Ratio of blue and white containers
(i) In mixture $A$,
$\text{Ratio of blue and white}=\frac{3}{4}=0.75$.
(ii) In mixture $B$,
$\text{Ratio of blue and white}=\frac{3}{3}=1$.
(iii) In mixture $C$,
$\text{Ratio of blue and white}=\frac{3}{3}=1$.
(iv) In mixture $D$,
$\text{Ratio of blue and white}=\frac{2}{5}=0.4$.
(v) In mixture $E$,
$\text{Ratio of blue and white}=\frac{6}{1}=6$.
(vi) In mixture $F$,
$\text{Ratio of blue and white}=\frac{4}{2}=2$.


(vii) In mixture $G$,
$\text{Ratio of blue and white}=\frac{3}{3}=1$.
(viii) In mixture $H$,
$\text{Ratio of blue and white}=\frac{4}{3}=1.33$.
On comparing, ratios of blue and white containers, $\text{Mixture D}<\text{Mixture A}<\text{Mixture B}=\text{Mixture C}=\text{Mixture G}<\text{Mixture H}<\text{Mixture F}<\text{Mixture E}$
$\therefore 0.4<0.75<1=1=1<1.33<2<6$
Hence, from the above all mixture, mixture $D$ is the lightest among them.

Calculate the number of blue and white containers
Given, $\text{Total number of container required for painting}=105$
Mixture $D$ is the lightest shade and has $2$ blue and $5$ white container.
$\therefore \text{Number of blue containers required for painting}=\frac{2}{7}\times 105=2\times 15=30$
$\therefore \text{Number of white containers required for painting}=\frac{5}{7}\times 105=5\times 15=75$
Hence, Number of blue and white containers required are $30$ and $75$ respectively to paint building in lightest blue color.