Question

A man saves $₹ 135 /-$ in the first year, $₹ 150 /$ - in the second year and in this way he increases his savings by $₹ 15 /-$ every year. In what time will his total savings be $₹ 5550 /-$ ?

• A. 20 years
• B. 25 years
• C. 30 years
• D. 35 years

Answer 1

Answer: (A)

Given statement makes an AP series where, $a =₹ 135$,
$d =₹ 15$ and $S _{ n }=₹ 5550$
Let total savings be $₹ 5550$ in $n$ years
So, $S_{n}=\frac{n}{2}[2 a+(n-1) d]$
$5550=\frac{ n }{2}[2 \times 135+( n -1) 15]$
$\Rightarrow 11100= n [270+15 n -15]$
$\Rightarrow 15 n ^{2}+255 n -11100=0$
$\Rightarrow n ^{2}+17 n -740=0$
$\Rightarrow n ^{2}+37 n -20 n -740=0$
$\Rightarrow ( n +37)( n -20)=0$
$n =20 (\because n \neq-37)$