Question

please answer me urgent need help​

Answer 1

EXPLANATION.

Mr. Gulati had a recurring deposit account = ₹ 300 per months.

Rate of interest = 12%.

Maturity value of this account is = ₹ 8100.

As we know that,

Let the maturity period = n.

Money deposit every months = P.

Rate of interest per annum = r.

$\sf I = P \times \dfrac{n(n + 1)}{24} \times \dfrac{r}{100}$

Put the values in the equation, we get.

⇒ I = 300 x n(n + 1)/24 x 12/100.

⇒ I = 3 x n(n + 1)/2.

⇒ I = 1.5n(n + 1).

Maturity value = 300 x n = 300n.

⇒ 300n + 1.5n² + 1.5n.

Maturity value = ₹ 8100.

⇒ 300n + 1.5n² + 1.5n = 8100.

⇒ 300n + 1.5n² + 1.5n - 8100 = 0.

⇒ 1.5n² + 301.5n - 8100 = 0.

⇒ n² + 201n - 5400 = 0.

Factorizes the equation into middle term splits, we get.

⇒ n² + 225n - 24n - 5400 = 0.

⇒ n(n + 225) - 24(n + 225) = 0.

⇒ (n - 24)(n + 225) = 0.

⇒ n = 24  and   n = -225.

⇒ n ≠ -225.

⇒ n = 24. months.

⇒ time = 2 years.

Option [B] is correct answer.