Question

Find the odd one out
\[(a)\] \[54:62\]
\[(b)\] \[28:32\]
\[(c)\] \[21:24\]
\[(d)\] \[14:16{\text{ }}\]

Answer 1

Hint: Ratio is nothing but a relationship between two numbers which shows how much one of the quantities is greater than the other. For example, we have \[6\] toffees and \[4\] chocolates in a box, then the ratio of toffees to chocolates is 6:4 whereas the ratio of chocolates to toffees is \[4:6\].

Complete step-by-step answer:
We are given that we have to find the odd one out. As we know ratio is division of 2 quantities and odd one out means after taking common we have to simplify the ratio like, we are given 4 options
\[\left( a \right)\;\;\;54:62{\text{ }}\left( b \right){\text{ }}28:32{\text{ }}\left( c \right){\text{ }}21:24{\text{ }}\left( d \right){\text{ }}14:16\]
In option \[\left( a \right)\]\[54:62\] implies \[\dfrac{{54}}{{62}}\], taking 2 common from numerator and denominator, we get\[\dfrac{{54}}{{62}} = \dfrac{{2 \times 27}}{{2 \times 31}} = \dfrac{{27}}{{31}}\]
2 gets cancel from numerator and denominator
\[\left( b \right){\text{ }}28:32{\text{ }}\]implies \[\dfrac{{28}}{{32}}\], taking 4 common from numerator and denominator, we get
\[\dfrac{{4 \times 7}}{{4 \times 8}} = \dfrac{7}{8}\]
Here, 4 gets canceled from the numerator and denominator.
\[\left( c \right){\text{ }}21:24{\text{ }}\]implies \[\dfrac{{21}}{{24}}\], taking 3 common from numerator and denominator, we get
\[\dfrac{{3 \times 7}}{{3 \times 8}} = \dfrac{7}{8}\]
Here, 4 gets canceled from the numerator and denominator.
 \[\left( d \right){\text{ }}14:16\] implies \[\dfrac{{14}}{{16}}\], taking 2 common from numerator and denominator, we get
\[\dfrac{{2 \times 7}}{{2 \times 8}} = \dfrac{7}{8}\] [2 gets cancel]

We have seen that in option \[\left( b \right),\left( c \right)\] and \[\left( d \right)\] ratio get reduced to \[\dfrac{7}{8}\] and in option \[\left( a \right)\] it is \[\dfrac{{27}}{{31}}\].\[\dfrac{{27}}{{31}}\] is an odd one and hence option \[\left( a \right)\] is the odd one out.

Note: Ratio of \[2\] quantities is unitless. We can also relate in our daily life such as the ratio of rupees to rupees is unitless and similarly, the ratio of weight to weight is unitless. Ratio \[a:b\] is not equal to \[5\]. For example, \[\dfrac{3}{4}\] is not equal to \[\dfrac{4}{3}\]. For calculating ratio, the units of numerator and denominator should be equal. For example if we want to find the ratio of \[3{\text{ }}kg\] to \[{\text{4gms}}\] .
So, we know \[1kg = 1000g\]
Therefore, \[3kg = 3 \times 1000g\]
\[ = 3000g\]
Ratio of \[3kg:4gm\] becomes \[3000kg:4g\]