Question

If $x$ and $y$ are in direct proportion, then $(x–1)$ and $(y–1)$ are also in direct proportion. State whether the statement is true (T) or false (F).

• A. True
• B. False

Answer 1

The correct option is B False

Two quantities $a$ and $b$ are said to be in direct proportion if they increase or decrease together. In other words, the ratio of their corresponding values remains constant. This means that, $\frac{a}{b}=k$

Given, $x$ and $y$ are directly proportional then, $\frac{x}{y}=k$

But, $\frac{x-1}{y-1}\ne k$

So, $(x–1)$ and $(y–1)$ are not directly proportional.

For example,

If $x=6$ and $y=8$ and they are in direct proportion then let's assume that $(x–1)$ and $(y–1)$ are also in direct proportion.

Then, $\frac{x}{y}=\frac{6}{8}$

And, $\frac{x-1}{y-1}=\frac{5}{7}$

Clearly, it is evident that $\frac{5}{7}\ne \frac{6}{8}$

So, $(x–1)$ and $(y–1)$ are not directly proportional.

Hence, the given statement is False.