Question

A sum of money at simple interest amounts to Rs. $600$ in $2$ years and to Rs. $800$ in $4$ years. The sum is:

• A. $100$
• B. $200$
• C. $300$
• D. $400$

Answer 1

The correct option is D $400$

$A_2=Rs600and{A}_4=Rs800$
In case of S.I.; $A_n=P+(n\times I)$ $\left[\text{here, n=no. of years and I=simple interest in one year}\right]$
$A_4=P+4I\Rightarrow 800=P+4I$ ...........eq(1)
$A_2=P+2I\Rightarrow 600=P+2I$ ..........eq(2)
subtracting eq(2) from eq(1) we get
$\Rightarrow 200=2I$
$\therefore I=100$
now substitutin $I=100$ in eq(2)
$\Rightarrow 600=P+2\times 100$
$\Rightarrow 600=P+200$
$\therefore P=Rs400$