Question

In a cricket coaching camp, 1200 children are trained, out of which 900 are selected for various matches. Ratio of non-selected children to the total number of children is
A. 300:120
B. 4:1
C. 1:4
D. 120:300

Answer 1

Hint: We first find the number of non-selected children and then find the fraction form of ratio of non-selected children to the total number of children. We take the simplified form of the fraction.

Complete step by step solution:
It is given that in a cricket coaching camp, 1200 children are trained out of which 900 are selected for various matches. The number of non-selected children is $1200-900=300$.
The ratio of non-selected children to the total number of children is $300:1200$.
The ratio has to be in its simplest form. The fraction form is $\dfrac{300}{1200}$.
For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}}$.
For our given fraction $\dfrac{300}{1200}$, the G.C.D of the denominator and the numerator is 300.
\[\begin{align}
  & 2\left| \!{\underline {\,
  300,1200 \,}} \right. \\
 & 2\left| \!{\underline {\,
  150,600 \,}} \right. \\
 & 3\left| \!{\underline {\,
  75,300 \,}} \right. \\
 & 5\left| \!{\underline {\,
  25,100 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5,20 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,4 \,}} \right. \\
\end{align}\]
The GCD is $2\times 2\times 3\times 5\times 5=300$.
Now we divide both the denominator and the numerator with 2 and get $\dfrac{{}^{300}/{}_{300}}{{}^{1200}/{}_{300}}=\dfrac{1}{4}$.
The simplified ratio form is $1:4$. The correct option is C.

Note: The ratio form gives us the unit of the different measurements. The relation between the measurements is derived from the ratio or its fraction form. Here the unit value is 300. This ratio is for the total, selected children and non-selected children.