Question

If $a$ and $b$ are positive integers, then the solution of the equation $ax=b$ will always be a

• A. positive number
• B. negative number
• C. $1$
• D. $0$

Answer 1

The correct option is A

positive number

Step 1: Explanation for the correct option:

Option (A): Given equation is $ax=b$$\Rightarrow$$x=\frac{b}{a}$

Clearly $x=\frac{b}{a}$ is the solution for the given equation.

Given that $a$ and $b$ are positive integers $\Rightarrow x$ is also positive.

Thus option (A) is correct.

Step 2: Explanation for the incorrect options:

Option (B): Clearly $x=\frac{b}{a}$ is the solution for the given equation

Given that $a$ and $b$ are positive integers $\Rightarrow x$ cannot be negative.

Thus option (B) is incorrect.

Option (C): $x=\frac{b}{a}$ and is no where mentioned that both are equal. So definitely $a\ne b$$\Rightarrow x\ne 1$

Thus option (C) is incorrect.

Option (D): $x=\frac{b}{a}$ and also given that $b$ is a positive integer $\Rightarrow b\ne 0$ and therefore $x\ne 0$

Thus option (D) is incorrect.

Hence, option(A) is correct.