A man save Rs. 400 more each years than he did the year before. If he saves Rs. 2000 in the first year after how mny years will his savings be more than Rs. 100000 altogether?

2000, 2000+400, 2000+400+400,....

This series is in arithmetic progression.

where a=2000 and d=400

Let n= number of years to get the sum of savings as Rs. ${S}_{n}=\frac{n}{2}(2a+(n-1\left)d\right)\phantom{\rule{0ex}{0ex}}100000=\frac{n}{2}(2*2000+(n-1\left)400\right)\phantom{\rule{0ex}{0ex}}100000=\frac{n}{2}(4000+400n-400)\phantom{\rule{0ex}{0ex}}100000=\frac{n}{2}(3600+400n)\phantom{\rule{0ex}{0ex}}100000=n(1800+200n)\phantom{\rule{0ex}{0ex}}Dividingby200\phantom{\rule{0ex}{0ex}}500=9n+{n}^{2}\phantom{\rule{0ex}{0ex}}{n}^{2}+9n-500=0\phantom{\rule{0ex}{0ex}}Solvingthisu\mathrm{sin}gquadraticformulaweget\phantom{\rule{0ex}{0ex}}n=18.3years\phantom{\rule{0ex}{0ex}}$.

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