What sum of money borrowed on 24th May will amount to ₹ 10,210.20 on 17th October of the same year at 5 percent per annum simple interest?

A = ₹ 10,210.20

R = 5%

To calculate time (T):

May = 7 days (31 -24)

Jun = 30 days

July = 31 days

August = 31 days

Sept = 30 days

Oct = 17 days

Total = 146 days

T = 146 days

= $\dfrac{146}{365}$ years

= $\dfrac{2}{5}$ years

Let the Principal amount be ₹ $P$.

As we know,

$\text{A = S.I. + P}\\[1em] \Rightarrow 10,210.20 = \text{S.I. + P}\\[1em] \Rightarrow \text{S.I.} = 10,210.20 - P \\[1em]$

$\because \text{S.I.} = ₹ \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow 10,210.20 - P = \Big(\dfrac{P \times 5 \times 2}{5 \times 100}\Big)\\[1em] \Rightarrow 10,210.20 - P = \Big(\dfrac{P \times 2}{100}\Big)\\[1em] \Rightarrow 10,210.20 - P = \dfrac{P}{50}\\[1em] \Rightarrow 10,210.20 = \dfrac{P}{50} + P\\[1em] \Rightarrow 10,210.20 = \dfrac{P}{50} + \dfrac{50P}{50}\\[1em] \Rightarrow 10,210.20 = \dfrac{(P + 50P)}{50}\\[1em] \Rightarrow 10,210.20 = \dfrac{51P}{50}\\[1em] \Rightarrow P = \dfrac{10,210.20 \times 50}{51}\\[1em] \Rightarrow P = \dfrac{510510}{51}\\[1em] \Rightarrow P = 10,010$

Hence, the Principal amount be ₹ 10,010.