Question

We need to create equivalent fractions using alphabets instead of numbers. This will be used as a security code.

Example:

$\frac{A}{B}=\frac{1}{2}\frac{\text{Position number of A in all the alphabets}}{\text{Position number of in all the alphabets}}$

Select the code whose equivalent fractions are formed correctly.

• A. $\frac{D}{G}=\frac{H}{O}$
• B. $\frac{G}{N}=\frac{A}{C}$
• C. None of the above
• D. $\frac{A}{J}=\frac{B}{T}$

Answer 1

The correct option is D $\frac{A}{J}=\frac{B}{T}$

To check if a fraction is an equivalent fraction of the original fraction, we need to check whether the numerator and denominator of the equivalent fraction is a multiple of the numerator and denominator of the original fraction.

First option says,

$\frac{G}{N}=\frac{A}{C}$
$\frac{G}{N}=\frac{7}{14},\frac{A}{C}=\frac{1}{3}$

$14$ is not a multiple of $3$. Hence, $\frac{G}{N}=\frac{A}{C}$ are not equivalent fractions.

Second option says,

$\frac{A}{J}=\frac{B}{T}\text{or}\frac{1}{10}=\frac{2}{20}$

$\frac{1}{10}=\frac{1\times 2}{10\times 2}=\frac{2}{20}$

This means $\frac{2}{20}$ is an equivalent fraction of $\frac{1}{10}$ .

Third option says,

$\frac{D}{G}=\frac{H}{O}$

$\frac{D}{G}=\frac{4}{7},\frac{H}{O}=\frac{8}{15}$

$15$ is not a multiple of $7.$

Hence, $\frac{G}{N}=\frac{A}{C}$ are not equivalent fractions.

So, only $\frac{A}{J}$ and $\frac{B}{T}$ are equivalent fractions.