Question

Meena has a cumulative deposit amount of ₹ 400 per month at 10% per annum simple interest. If she

gets ₹ 26550 at the time of maturity. Find the total time for which the account was held ?​

Answer 1

$\sf{Let \: the \: amount \: be \: held \: for \: x \: months}$

$\sf\red{I = 400 \times \frac{x(x + 1)}{2 \times 12} \times \frac{10}{100} = \frac{5x(x + 1)}{3}}$

$\small\rm{Total \: amount \: deposited =400\times x= 400x}$

$\small\rm \:Amount \: on \: maturity = 400x + \frac{5 \times (x + 1)}{3}$

$\rm= \frac{{5x}^{2} + 1205x}{3} = 26550$

$\bf\implies \: {5x}^{2} + 1205 - 79650 = 0$

$\bf\implies{ {x}^{2} + 241 - 15903 = 0}$

$\bf\implies{(x - 54)(x + 295) = 0}$

$\bf\implies{x = 54, - 295,x ≠ - 295}$

$\sf\red{ x = 54 \: months}$

Hope you understand now !!