M L Aggarwal Solutions for Chapter: Playing With Numbers, Exercise 6: Check Your Progress

In a $2$-digit number, sum of digits is $7$. If the difference of $2$-digit number and number obtained by reversing the digits is $9$, then find the number.

Find the values of the letters and give reasons for the steps involved:

$$\begin{gathered} \begin{array}{ccc} \mathrm{A}& \mathrm{B}& 2\\ +& 2& \mathrm{A}\end{array} \\ \overline{ \underline{\begin{array}{ccc}\mathrm{A}& \mathrm{A}& 8\end{array}}} \end{gathered}$$ 

Find the values of the letters and give reasons for the steps involved:

$$\begin{gathered} \begin{array}{cccc} & 4& \mathrm{A}& \mathrm{B}\\ +& \mathrm{A}& \mathrm{B}& 7\end{array} \\ \underline{\overline{\begin{array}{cccc}1& 0& 2& 3\end{array}}} \end{gathered}$$

Find the values of the letters and give reasons for the steps involved:

$$\begin{gathered} \begin{array}{cccc} & \mathrm{A}& \mathrm{A}& \mathrm{B}\\ & & \times & \mathrm{B}\end{array} \\ \underline{\overline{\begin{array}{cccc}& 8& 8& \mathrm{A}\end{array}}} \end{gathered}$$

Check the divisibility of the number $23565$ by $5$ or $10$.

Check the divisibility of the number $45270$ by $5$ or $10$.

Check the divisibility of the number $47596$ by $4$ or $8$.

Check the divisibility of the number $593024$ by $4$ or $8$.