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NMTC doubt questions

I recently appeared nmtc final round junior and these are the questions in which i have doubt. Please upload the solution if you know the answer
Q.1 a,b,c are positive real numbers. Find the minimum value of \( \frac{a+3c}{a+2b+c} \)+ \( \frac{4b}{a+b+2c} \)- \( \frac{8c}{a+b+3c} \) I got the answer \( \frac{2}{5} \) . Is it correct?

Q.2 show that for any natural number n, there is a positive integer all of whose digits are 5 or 0 and is divisible by n. I have totally no idea how this one is done , and i ended up just bluffing some answer in the end. thanks in advance for the solution

Note by Sayantan Dhar
8 months ago

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Question 1: The minimum value is \(12\sqrt2 - 17\) and it occurs when \((a,b,c) = \left( \dfrac32 - \sqrt2, \dfrac1{\sqrt2} - \dfrac12 , \dfrac1{\sqrt2} \right) \). Pi Han Goh · 8 months ago

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@Pi Han Goh can you please post the detailed solution Sayantan Dhar · 8 months ago

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