Question

A sum of money lent at simple interest amounts to $Rs3224$ in $2$ years and $Rs4160$ in $5$ years. Find the sum and the rate of interest.

• A. $Rs.2500$
• B. $Rs.2000$
• C. $Rs.2600$
• D. $Rs.1600$

Answer 1

Answer: (C)

$Rs.2600$

Let, Principle be $Rs.P$ and Rate be $R$% p.a

$\because$ Amount $A=P(1+\frac{RT}{100})$

If a certain sum amounts to $Rs.3224$ in $2$ years, then

$3224=P(1+\frac{2R}{100})$........(i)

If a certain sum amounts to $Rs.4160$ in $5$ years, then

$4160=P(1+\frac{5R}{100})$........(ii)

$\frac{\left(ii\right)}{\left(i\right)}⟹\frac{4160}{3224}=\frac{P(1+\frac{5R}{100})}{P(1+\frac{2R}{100})}$

$⟹\frac{4160}{3224}=\frac{(1+\frac{5R}{100})}{(1+\frac{2R}{100})}$

$⟹\frac{40}{31}=\frac{100+5R}{100+2R}$

$⟹40(100+2R)=31(100+5R)$

$⟹4000+80R=3100+155R$

$⟹4000-3100=155R-80R$

$⟹900=75R$

$⟹R=\frac{900}{75}$

$\therefore R=12$

From, $\left(i\right)⟹3224=P(1+\frac{2R}{100})$

$⟹3224=P(1+\frac{24}{100})$

$⟹3224=P\left(\frac{124}{100}\right)$

$⟹P=3224\times \frac{100}{124}$

$\therefore P=Rs.2600$