I had ₹ $10000$ with me. Out of this money I lent some money to A for $2$ years @ $15\%$ simple interest. I lent the remaining money to B for an equal number of years @ $18\%$ simple interest. After $2$ years, I found that A had given me ₹ $360$ more as interest as compared to B. The amount of money which I had lent to B must have been

### Concept & Simple Interest Difference When a total principal is split into two unknown parts and the difference between their simple interests is given, set up a linear equation representing the difference to solve for one of the parts. $$ SI = \frac{P \times R \times T}{100} $$ ### Step-by-Step Solution - Let the money lent to B be $x$. - Then, the money lent to A is $(10000 - x)$. - Time ($T$) for both = $2$ years. - Rate for A ($R_A$) = $15\%$, Rate for B ($R_B$) = $18\%$. - Simple Interest from A = $\frac{(10000 - x) \times 15 \times 2}{100} = \frac{30(10000 - x)}{100} = \frac{3(10000 - x)}{10}$ - Simple Interest from B = $\frac{x \times 18 \times 2}{100} = \frac{36x}{100} = \frac{9x}{25}$ - We are given that Interest from A - Interest from B = ₹ $360$. - $\frac{3(10000 - x)}{10} - \frac{9x}{25} = 360$ - Multiply the entire equation by the LCM of $10$ and $25$, which is $50$, to clear denominators: - $5 \times 3(10000 - x) - 2 \times 9x = 360 \times 50$ - $15(10000 - x) - 18x = 18000$ - $150000 - 15x - 18x = 18000$ - $150000 - 18000 = 33x$ - $132000 = 33x$ - $x = \frac{132000}{33} = 4000$ - The money lent to B is ₹ $4000$. ### Exam Strategy & Shortcut Use the total percentage of interest over 2 years directly: $30\%$ for A and $36\%$ for B. $30\% \text{ of } (10000 - x) - 36\% \text{ of } x = 360$ $3000 - 0.3x - 0.36x = 360$ $2640 = 0.66x \Rightarrow x = 4000$. This skips fraction handling entirely. ### Common Pitfall Setting the equation backwards as $(Interest from B) - (Interest from A) = 360$. Carefully read which one yielded "more" interest. ### Final Answer Therefore, the correct answer is **₹ 4000**.