Question 1: \(\text { Give } \mathrm{n}=\overline{7 a 5}+\overline{8 b 4} \text {. Know a }-\mathrm{b}=6 \text { and } \mathrm{n} \text { divisible by } 9 \text {. Find a and }\)

n is divisible by 9

\(\begin{aligned} &\Rightarrow 7 a 5+\overline{8 b 4} \text { divisible by } 9\\ &\Rightarrow 7+a+5+8+b+4 \text { divisible by for } 9\\ &\Rightarrow 24+a+b \text { divisible by } 9 \text {. } \end{aligned}\)

\(\begin{aligned} &\text { Which } \mathrm{a}, \mathrm{b} \leq 9 \Rightarrow \mathrm{a}+\mathrm{b} \leq 18 \\ &\Rightarrow \mathrm {a}+\mathrm{b}=3 \text { or } \mathrm{a}+\mathrm{b}=12 . \\ &*\mathrm{a}+\mathrm{b}=3 \\ & \Rightarrow \mathrm{a}=(3+6): 2=9 / 2 \text { not in } \mathrm{N} \text { (type) } \end{aligned}\)

\(\begin{aligned} &*\mathrm{a}+\mathrm{b}=12 \\ &\Rightarrow \mathrm{a}=(12+6): 2=9 ; \mathrm{b}=9 -6=3(\text { select }) \\ &\text { So } \mathrm{a}=9 \text { and } \mathrm{b}=3 \end{aligned}\)

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