Question

If the original size of an image is $540\times 680$, which of the following image sizes cannot be achieved, to ensure that there is no deformation in the picture?

• 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 $\frac{540}{680}$ ...(i)

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 $\frac{(540\times 2)}{(680\times 2)}=\frac{1080}{1360}$

Proceeding in a similar way, we observe that the original fraction cannot be written as $\frac{123}{164}$ and hence this picture size cannot be achieved without compromising the picture quality.