On what date will ₹ 1,950 lent on 5th January, 2011 amount to ₹ 2,125.50 at 5 percent per annum simple interest?

Given:

P = ₹ 1,950

A = ₹ 2,125.50

R = 5%

Let the time be $t$

As we know,

$\text{A = P + S.I.}\\[1em] \Rightarrow ₹ 2,125.50 = ₹ 1,950 + S.I.\\[1em] \Rightarrow S.I. = ₹ 2,125.50 - ₹ 1,950 \\[1em] \Rightarrow S.I. = ₹ 175.50$

And,

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow 175.50 = \Big(\dfrac{1,950 \times 5 \times t}{100}\Big)\\[1em] \Rightarrow 175.50 = \dfrac{9,750t}{100}\\[1em] \Rightarrow t = \dfrac{175.50 \times 100}{9750}\\[1em] \Rightarrow t = \dfrac{9}{5}\\[1em] \Rightarrow t = 1\dfrac{4}{5}$

$1\dfrac{4}{5}$ years means 1 years and 292 days (∵ $\dfrac{4}{5} \ \times 365 = 292$).

As the money was lent on 5th January, 2011,

1 year from 5th January, 2011 = 5th January, 2012

And 292 days = Jan (26 days) + Feb (29 days) + March (31 days) + April (30 days) + May (31 days) + June (30 days) + July (31 days) + Aug (31 days) + Sept (30 days) + Oct (23 days)

Hence, the required date is 23^rd October, 2012.