Question

Assertion: Three rational numbers between $\frac{2}{5}\mathrm{and}\frac{3}{5}\mathrm{are}\frac{9}{20},\frac{10}{20}\mathrm{and}\frac{11}{20}$.
Reason: A rational number between two rational numbers p and q is $\frac{1}{2}\left(p+q\right)$.
(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.

Answer 1

(a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
$$\begin{gathered} \mathrm{Rational}\mathrm{number}\mathrm{between}\frac{2}{5}\mathrm{and}\frac{3}{5}: \\ \frac{\frac{2}{5}+\frac{3}{5}}{2}=\frac{1}{2}=\frac{10}{20} \\ \mathrm{Rational}\mathrm{number}\mathrm{between}\frac{2}{5}\mathrm{and}\frac{10}{20}: \\ \frac{\frac{2}{5}+\frac{10}{20}}{2}=\frac{18}{40}=\frac{9}{20} \\ \mathrm{Rational}\mathrm{number}\mathrm{between}\frac{3}{5}\mathrm{and}\frac{10}{20}: \\ \frac{\frac{3}{5}+\frac{10}{20}}{2}=\frac{22}{40}=\frac{11}{20} \end{gathered}$$

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