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  4. A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

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Q. A man saves Rs. $200$ in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. $40$ more than the saving of immediately previous month. His total saving from the start of service will be Rs. $11040$ after

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Solution:

Total savings $=200+200+200+240+280+\ldots$ to $n$ months $=11040$
$\Rightarrow 400+\frac{n-2}{2}(400+(n-3) \cdot 40)=11040$
$\Rightarrow (n-2)(140+20 n)=10640$
$\Rightarrow 20 n^{2}+100 n-280=10640$
$\Rightarrow n^{2}+5 n-546=0$
$\Rightarrow (n-21)(n+26)=0$
$\Rightarrow n=21$ as $n \neq-26$