103
Prerna saves ₹32 during the first month, ₹36 in the second month and ₹40 in the third month. If she continues to save in this manner, in how many months will she save ₹2,000?
Show SolutionHide Solution↓
ATQ,
$32+36 +40 + ..... = 2,000$
$a = 32, d =4$ ($\frac{1}{2} + \frac{1}{2}$)
Let 'n' be the number of months.
$S_n = 2000$
$\frac{n}{2}[2(32) + (n - 1) 4] = 2000$ (1)
$n^2 + 15n - 1000 = 0$ (1)
$n^2 + 40n - 25n - 1000 = 0$
$(n + 40) (n - 25) = 0$ (1)
$\Rightarrow n = -40, n = 25$
(rejecting)
$\therefore n = 25$ (1)
So, Prerna will save ₹2,000, in $25$ months.
$32+36 +40 + ..... = 2,000$
$a = 32, d =4$ ($\frac{1}{2} + \frac{1}{2}$)
Let 'n' be the number of months.
$S_n = 2000$
$\frac{n}{2}[2(32) + (n - 1) 4] = 2000$ (1)
$n^2 + 15n - 1000 = 0$ (1)
$n^2 + 40n - 25n - 1000 = 0$
$(n + 40) (n - 25) = 0$ (1)
$\Rightarrow n = -40, n = 25$
(rejecting)
$\therefore n = 25$ (1)
So, Prerna will save ₹2,000, in $25$ months.