Question

The simple interest on a sum of money will be Rs. $500$ after $10$ years. If principal is double after $5$ years., the total interest at the end of the $10$ th year will be

• A. Rs. $350$
• B. Rs. $650$
• C. Rs. $500$
• D. Rs. $750$

Answer 1

Answer: (D)

Rs. $750$

In first condition,

Given, Simple interest, $I=$ Rs. $500$
Time $T=10$ years
We know, $I=\frac{PTR}{100}$
$100I=PTR$ ....($P=$ Principal, $R=$ Rate)
$PR=\frac{100I}{T}$
$PR=\frac{100I}{10}=10\times 500=$ Rs. $5000$ .......(i)
To make principal $P$ double in $5$ years, it must have to have $P$ as an interest.
So, Principal $=P$,
Interest $=P$
Time $=5$ years
$I=\frac{PTR}{100}$
$100\times P=P\times 5\times R$
$R=20\%$ per year
Now, using equation (1) , we get
$PR=5000$
$P=\frac{5000}{20}=$ Rs. $250$
Principal Rs. $250$ has become double in $5$, then it must be Rs. $1000$ in $10$ years.
So, total interest $=1000-250=$ Rs. $750$