Question

A certain sum amounts to Rs.3,825 in 4 years and to Rs.4,050 in 6 years. Find the rate percent and the sum.

• A. $3\frac{1}{3}\%$ , $3,375$ Rs.
• B. $2\frac{1}{3}\%$ , $3,375$ Rs.
• C. $3\frac{1}{2}\%$ , $3,825$ Rs.
• D. $4\frac{1}{3}\%$, $3,825$ Rs.

Answer 1

Answer: (A)

$3\frac{1}{3}\%$ , $3,375$ Rs.

We know that,
$Amount,A=P+\frac{PNR}{100}$

For the first situation,
$3,825=P+\frac{P\times 4\times R}{100}$
$=>3,825=P+\frac{4PR}{100}$ --- (1)

And for the second situation,
$4,050=P+\frac{P\times 6\times R}{100}$
$=>4,050=P+\frac{6PR}{100}$ --- (2)

Now, subtracting eqn 1 from 2, we get
$225=\frac{2PR}{100}$
$=>PR=11,250$

Putting the value of $PR$ in equation 1, we get
$=>3,825=P+\frac{4\times 11,250}{100}$
$=>3,825=P+\frac{4\times 11,250}{100}$
$=>3,825=P+450$
$=>P=3,375$

And since $PR=11,250$

$=>R=\frac{11,250}{3,375}=3\frac{1}{3}$ %