Question

A certain sum of money lent out at simple interest amounts to rs. 690 in 3 years and rs. 750 in 5 years. Find the sum lent

Answer 1

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Answer 2

Answer:

Rs.600

Step-by-step explanation:

Amount = Rs.690

Time = 3 years

Formula : $A=P(1+\frac{rt}{100})$

Substitute the values

$690=P(1+\frac{3r}{100})$

$690=P(\frac{100+3r}{100})$

$\frac{690}{\frac{100+3r}{100}}=P$ --1

Now Amount = Rs.750

Time = 5 years

$750=P(1+\frac{r5}{100})$

$750=P(\frac{100+5r}{100})$

$\frac{750}{(\frac{100+5r}{100})}=P$  -2

Equating 1 and 2

$\frac{750}{(\frac{100+5r}{100})}=\frac{690}{\frac{100+3r}{100}}$

$750(\frac{100+3r}{100})=690(\frac{100+5r}{100})$

$r=5$

Now substitute r = 5 in 1

$\frac{690}{\frac{100+3(5)}{100}}=P$

$600=P$

Hence the sum lent is Rs.600