Question

A sum of money becomes six times at simple interest. The rate of interest is $5\%$ per annum. At what rate per cent will it become twelve fold ?

• A. $7\%$ pa
  
• B. $9\%$ pa
• C. $11\%$ pa
• D. $13\%$ pa

Answer 1

The correct option is C $11\%$ pa

Let the principal P $=$ Rs. $x$.

Then, Amount (A) $=$ Rs. $6x$

Rate R $=5\%$ p.a.

$\therefore S.I.=A-P$

$=$ Rs. $6x-$ Rs. $x=$Rs. $5x$

Formula for simple interest $S.I=\frac{P.T.R}{100}$

$\therefore$ Time $T=\frac{S.I.\times 100}{P\times R}$

$=\frac{5x\times 100}{x\times 5}=100$ years

Now, $P=$ Rs. $x$, $A=$.Rs. $12x,T=100$ years,

S.l. $=$ Rs. $12x-$ Rs. $x$ $=$ Rs. $11x$

$\therefore R=\frac{S.I.\times 100}{P\times T}=\frac{11x\times 100}{x\times 100}=11\%p.a.$