Question

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3. How many numbers of two digits are divisible by 5?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{list}\mathrm{of}2-\mathrm{digit}\mathrm{numbers}\mathrm{that}\mathrm{are}\mathrm{divisible}\mathrm{by}5\mathrm{is}: \\ 10,15,20,..........,95 \\ \mathrm{The}\mathrm{above}\mathrm{list}\mathrm{forms}\mathrm{an}\mathrm{AP}\mathrm{with}\mathrm{first}\mathrm{term},\mathrm{a}=10\mathrm{and}\mathrm{common}\mathrm{difference},\mathrm{d}=5 \\ \mathrm{Let}{\mathrm{a}}_{\mathrm{n}}=95 \\ \Rightarrow \mathrm{a}+\left(\mathrm{n}-1\right)\mathrm{d}=95 \\ \Rightarrow 10+\left(\mathrm{n}-1\right)\times 5=95 \\ \Rightarrow 5\left(\mathrm{n}-1\right)=85 \\ \Rightarrow \mathrm{n}-1=17 \\ \Rightarrow \mathrm{n}=18 \\ \mathrm{There}\mathrm{are}18\mathrm{two}-\mathrm{digit}\mathrm{numbers}\mathrm{that}\mathrm{are}\mathrm{divisible}\mathrm{by}5. \end{gathered}$$