Question

Rupees 4000 amount to Rs.5000 in 8 years; in what time will Rs.2100 amount to Rs.2800 at the same rate?

Answer 1

In first case :

A = Rs.5000

P = Rs.4000

I = A − P

= Rs.5000 − Rs.4000

= Rs.1000

T = 8 years

∵ SI = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$

∴ R =${\displaystyle \frac{100\times \text{I}}{\text{P}\times \text{T}}}$

R ${\displaystyle =\frac{100\times 1000}{4000\times 8}}$

R ${\displaystyle =\frac{25}{8}\%}$

In the second Case :

A = Rs.2800

P = Rs.2100

I = Rs.2800 − Rs.2100 = Rs.700

R = ${\displaystyle \frac{25}{8}\%}$

∴ T =${\displaystyle \frac{100\times \text{I}}{\text{P}\times \text{R}}}$

${\displaystyle =\frac{100\times 700}{2100\times \frac{25}{8}}}$

${\displaystyle =\frac{100\times 700\times 8}{2100\times 25}}$

${\displaystyle =\frac{32}{3}}$years

${\displaystyle =10\frac{2}{3}}$ years

${\displaystyle =10\frac{2}{3}\times 12}$ months = ${\displaystyle 10\frac{24}{3}}$ months

= 10 years 8 months