Question

On what sum, does the difference between the compound interest and the simple interest for 3 years at 10% is Rs.31 ?

• A. Rs.1000
• B. Rs.1100
• C. Rs.1200
• D. Rs.1300

Answer 1

The correct option is A Rs.1000

Let the sum be Rs.100 Then
$C.I.=100{(1+\frac{10}{100})}^3-100=100\times {\left(\frac{11}{10}\right)}^3-100=100\times \frac{1331}{1000}-100$
= Rs.133.10 - Rs.100 = Rs.33.10 $S.I.=\frac{100\times 3\times 10}{100}=Rs.30$
$\therefore$ Difference = Rs.33.10 - Rs.30 = Rs.3.10 Now, Rs.3.10 is the difference when the sum is Rs.100
$\therefore$ Rs.31 is the difference when the sum is Rs.$(\frac{100}{3.10}\times 31)=Rs.1000$