Question

At certain rate of simple interest. Rs. 1,000 becomes Rs. 2,000 in 5 years and at a different rate of interest it becomes Rs. 3,000 in 12 years. The better rate of interest is-

• A. 24%
• B. 15%
• C. 20%
• D. 16.67%

Answer 1

The correct option is D 16.67%

Let rate for $1^{st}$ condition $=r_1$ and for $2^{nd}$ condition be $=r_2$ respectively.

For Part 1

$P=1000$

$r=r_1$

$t=5$

$S.I=A-P$

$=2000-1000$

$=1000$

$\therefore 1000=\frac{1000\times r_1\times 5}{100}(SI=\frac{PTR}{100})$

$\Rightarrow r_1=\frac{100}{5}=20$

For Part 2

$P=1000$

$r=r_2$

$t=12$

$A=3000$

$\therefore S.I=A-P$

$=3000-1000$

$=2000$

$\therefore 2000=\frac{1000\times r_2\times 12}{100}(\frac{PTR}{100}=S.I)$

$\Rightarrow r_2=\frac{2\times 100}{12}$

$=16.67$%

Since $r_2>r_1$

$\therefore$ Better rate of interest is $16.67$%.