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)

$21$ months

Answer 2

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 $n \neq-26$