MAT Exam 2020 Paper

Concept:Use Simple Interest on two parts lent for different periods and match the given ratio.Explanation:Let the first part, lent at $6\%$ per six months, be ₹ $x$.Then the second part, lent at $5\%$ per annum after 1 year, is ₹ $(38800-x)$.First part is invested for 3 years, that is, for $6$ half-years.Interest on first part:$$I_1=\frac{x \times 6 \times 6}{100}=\frac{36x}{100}$$Second part is lent 1 year later, so it earns interest for only $2$ years.Interest on second part:$$I_2=\frac{(38800-x)\times 5\times 2}{100}=\frac{10(38800-x)}{100}$$Given ratio:$$\frac{I_1}{I_2}=\frac{5}{4}$$So,$$\frac{36x}{10(38800-x)}=\frac{5}{4}$$Simplify:$$\frac{18x}{5(38800-x)}=\frac{5}{4}$$$$72x=25(38800-x)$$$$72x=970000-25x$$$$97x=970000$$$$x=10000$$Thus, the first part is ₹ $10000$.Second part:$$38800-10000=28800$$Answer:₹ $28800$Option B.