Question

A sum is divided between A and B in the ratio of 1:2. A purchased a car from his part, which depreciates $\frac{100}{7}$ $\%$ 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 (approx)?

• A. 20 %
• B. 25 %
• C. 28 %
• D. 18 %

Answer 1

The correct option is A

20 %

Let the total sum be Rs. 300 which is divided such that A will get Rs. 100 and B gets Rs. 200

Depreciation percentage =$\left(\frac{100}{7}\right)$ %

Value of car after 2 years

= Rs. 100 ${[1-\frac{\frac{100}{7}}{100}]}^2$

= Rs. 100${[1-\left(\frac{1}{7}\right)]}^2$

= Rs. 100${\left[\frac{6}{7}\right]}^2$

=$Rs.100\times \left(\frac{6}{7}\right)\times \left(\frac{6}{7}\right)$

≈ Rs. 73

Interest percentage = $20\%$

B’s amount after 2 years

=Rs.200${\left(\frac{1+20}{100}\right)}^2$

=Rs.200${\left(\frac{6}{5}\right)}^2$

= Rs.200$\times \frac{6}{5}\times \frac{6}{5}$

= Rs. 288

Increase = $Rs.288\dotplus Rs.73-Rs.300$ = Rs. 61

Required percentage = $\left(\frac{61}{300}\right)\times 100\%$= $20\%$