Question

Mr. Gupta has taken a debt at the rate of $7\frac{1}{2}$% p.a. After $3\frac{1}{2}$ years,he redeems himself the debt by paying a sum of Rs. $4545$. Find the sum borrowed by Mr. Gupta.

Answer 1

Let the sum borrowed by Mr. Gupta$=x$

After $3\frac{1}{2}$ years, simple interest would be:-

$=\frac{x\times \left(7\frac{1}{2}\right)\times \left(3\frac{1}{2}\right)}{100}$ $\{S.I=\frac{P\times R.T}{100}\}$

$P=$ Principle

$R=$ Rate

$T=$ Time

$=\frac{x\times \left(\frac{15}{2}\right)\times \left(\frac{7}{2}\right)}{100}$

$=\frac{105x}{400}$

$=\frac{21x}{80}$

So, $4505=x+\frac{21x}{80}$

$\Rightarrow 4505=\frac{101x}{80}$

$\Rightarrow x=\frac{4505\times 80}{101}$

$=3568.32$.