Question

If the original size of a picture is $540\times 680$, then which of the following picture sizes is not in proportion with the original size?

• A. $135\times 170$
• B. $27\times 34$
• C. $1080\times 1360$
• D. $123\times 164$

Answer 1

The correct option is D $123\times 164$

To solve this question, we need to check how $540\times 680$ can be reduced or expressed as higher fractions without changing the value of their ratio.

We know that if numerator and denominator of a fraction are multiplied or divided by the same number, then it won't change their ratio.

Our fraction is
$\frac{540}{680}...\left(i\right)$

On dividing the numerator and denominator of (i) by 4, we get
$\frac{(540÷4)}{(680÷4)}=\frac{135}{170}$

Similarly, on dividing the numerator and denominator of (i) by 5, we get,
$\frac{27}{34}$

Similarly, on multiplying the numerator and denominator of (i) by 2, we get,
$\frac{(540\times 2)}{(680\times 2)}=\frac{1080}{1360}$

Going in a similar way, we observe that the original fraction can not be written as $\frac{123}{164}$ and hence this picture size is not in proportion with the original image size.