Question

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

• A. $21$ months
• B. $18$ months
• C. $19$ months
• D. $20$ months

Answer 1

Answer: (A)

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