Question

Find the greater ratio between \[7:16\] and \[17:27\]

Answer 1

Hint: First, we have to find the equivalence form for ratio \[a:b\] into the form of \[e:f\]. In the similar way, we have to find the equivalence for the ratio \[c:d\] into the form \[g:f\]. After obtaining the transformed form we should find the number which is greater among e and g. If e is greater than g, then \[a:b\] is greater than \[c:d\]. If g is greater than f, then \[c:d\] is greater than \[a:b\]. So, now let us compare \[a:b\] with \[7:16\] and let us compare \[c:d\] with \[17:27\].By doing the above process, we can get the required result.

Complete step-by-step answer:
Before solving the question, we should know how to find the greater ratio among \[a:b\]and \[c:d\]. First, we have to find the equivalence form for ratio \[a:b\] into the form of \[e:f\]. In the similar way, we have to find the equivalence form for ratio \[c:d\] into the form \[g:f\]. After obtaining the transformed form we should find the number which is greater among e and g. If e is greater than g, then \[a:b\] is greater than \[c:d\]. If g is greater than f, then \[c:d\] is greater than \[a:b\].
Now let us compare \[a:b\] with \[7:16\].
\[\Rightarrow \dfrac{a}{b}=\dfrac{7}{16}\]
Now let us multiply and divide with 27 on R.H.S.
\[\Rightarrow \dfrac{a}{b}=\dfrac{189}{432}.....(1)\]
Now let us compare \[e:f\] with \[189:432\].
\[\Rightarrow \dfrac{e}{f}=\dfrac{189}{432}.....(2)\]
Now let us compare \[c:d\] with \[17:27\].
\[\Rightarrow \dfrac{c}{d}=\dfrac{17}{27}\]
Now let us multiply and divide with 16 on R.H.S.
\[\Rightarrow \dfrac{c}{d}=\dfrac{272}{432}.....(3)\]
Now let us compare \[g:f\] with \[272:432\].
\[\Rightarrow \dfrac{g}{f}=\dfrac{272}{432}.....(4)\]
Now from equation (2), we get the value of e is equal to 189.
In the similar way, from equation (4), we get the value of g is equal to 273.
We know that 272 is greater than 189.
So, we can say that g is greater than e.
So, we can say that \[17:27\] is greater than \[7:16\].

Note: Students should be careful at calculation part of this question. If a small mistake is made, then it is not possible to get a correct final answer. So, one should do the calculation part in a perfect manner. This is also important to solve this problem. Students should be able to find the correct value of f. With respective values of f, we can find the value of e and g respectively. If anything went wrong, then the final answer will get interrupted.