# Assertion: Three rational numbers between

Question:

Assertion: Three rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$ are $\frac{9}{20}, \frac{10}{20}$ and $\frac{11}{20}$.

Reason: A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(p+q)$.

(a) Both Assertion and Reason are true and Reasom is a correct explanation of Assertion.
(b) Both Assertion and Reason and Reasom are true but Reasom is not a correct explanation of Assertion.
(c) Assertion is true and Reasom is false.
(d) Assertion is false and Reasom is true.

Solution:

(a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Rational number between $\frac{2}{5}$ and $\frac{3}{5}$ :

$\frac{\frac{2}{5}+\frac{3}{5}}{2}=\frac{1}{2}=\frac{10}{20}$

Rational number between $\frac{2}{5}$ and $\frac{10}{20}$ :

$\frac{\frac{2}{5}+\frac{10}{20}}{2}=\frac{18}{40}=\frac{9}{20}$

Rational number between $\frac{3}{5}$ and $\frac{10}{20}$ :

$\frac{\frac{3}{5}+\frac{10}{20}}{2}=\frac{22}{40}=\frac{11}{20}$

So, Assertion and Reason are correct (property of rational numbers). Also, Reason is the correct explanation of Assertion.