Question

In a tour, I spent every day as many ten rupee notes as the number of days I had been away from home. My total expenditure was Rs. 18,300. how long did I stay away from the home?

• A. 1 month
• B. 2 months
• C. 3 months
• D. 4 months

Answer 1

The correct option is B 2 months

Let man spend Rs. 10,20,30,.........

On $1^{st}{2}^{nd}{3}^{rd}$............ day respectively

ATQ

10+20+30........= 18300

$s_n=\frac{n}{2}(2a+(n-1\left)d\right)$

= $\frac{n}{2}\left(2\right(10)+(n-1\left)10\right)$ = 18300

=$\frac{n}{2}$[10n+10] = 18300

$5n^2$ +5n = 18300

$n^2$ +n -3660 = 0

$n^2$ +61n - 60n -3660 = 0

n(n - 61) - 60(n + 61) = 0

(n - 60) (n + 61) = 0, n = 60, n $\ne$ 61

n = 60 i.e. 2 months