Question

A sum is divided between A and B in the ratio of $1:2$. A purchased a car from his part, which depreciates $14\frac{2}{7}$% per annum and B deposited his amount in a bank, which pays him $20\%$ interest per annum compounded annually.By what percentage will the total sum of money increase after two years due to this investment pattern (approximately).

• A. $20\%$
• B. $26.66\%$
• C. $30\%$
• D. $25\%$

Answer 1

Answer: (A)

Let the total money be $Rs.x$

$A$ got $Rs.x/3$ and $B$ got $Rs.2x/3$

Depreciation percentag$=14\frac{2}{7}\%=\left(100/7\right)\%$

$A^{\prime }s$ value after $2$ years

$=\frac{x}{3}[1-\frac{100/7}{100}{]}^2=\frac{12x}{49}$

$B^{\prime }s$ value after $2$ years

$=\frac{2x}{3}[1+\frac{20}{100}{]}^2=\frac{24x}{25}$

Increment$=(\frac{12x}{49}+\frac{24x}{25})-x=\left(\frac{1476x}{1225}\right)-x=\frac{251x}{1225}$

Percentage of increment$=\frac{\left(251x/1225\right)}{x}\times 100=20\%$(approx).