Question

The simple interest on a certain sum of money for 4 years at 12% per annum is ₹ 50 more than the simple interest on the same sum for 3 years at 10% per annum. Find the sum.

• A.
  250.5 rupees
• B.
  277.7 rupees
• C.
  270 rupees
• D. 297 rupees

Answer 1

The correct option is B

277.7 rupees
Let the sum be p
Let $i_1$ be the interest on the sum p for 4 years at 12% per annum
$i_1=\frac{p\times 4\times 12}{100}$
Let $i_2$ be the interest on the sum p for 3 years at 10% per annum
$i_2=\frac{p\times 3\times 10}{100}$

Given that $i_1=50+i_2$
$\frac{p\times 4\times 12}{100}=50+\frac{p\times 3\times 10}{100}$
$\frac{48p}{100}-\frac{3p}{100}=50$
$\frac{p\times 18}{100}=50$
$p=\frac{100\times 50}{18}$
$p=₹277.70$