Question

The C.I. and S.I. on a sum of money for $2$ years is Rs. $210$ and Rs. $200$ respectively. If the rate of the interest is same, then sum and rate will be

• A. $1500,10\%$
• B. $1000,10\%$
• C. $1200,8\%$
• D. $800,15\%$

Answer 1

The correct option is B $1000,10\%$

S.I. for $2$ year $=$ Rs. $200$

$\therefore$ S.I. for $1$ year $=$ Rs. $100$

$\because$ C.I. and S.I. for $1$ year is equal

$\therefore$ C.I. for $1$ year $=$ Rs. $100$

$\therefore$ C.I for the $2^{nd}$ year $=$ Rs. $110$

Then S.I. on Rs. $200$ for $1$ year$=110-100=$ Rs. $10$

S.I. $=\frac{\text{PRT}}{100}$

$\Rightarrow R=\frac{\text{S.I.}\times 100}{PR}$

$\Rightarrow R=\frac{10\times 100}{100}=10\%$

Now time $=1$ year, $R=10\%$, S.I $=100$

$\therefore P=\frac{100\times 100}{10\times 1}=$ Rs. $1000$