Question : Equal sum of money are lent to X and Y at 7.5% per annum for 4 years and 5 years respectively. If the difference in interest, paid by them was Rs. 150, the sum lent to each was:
Option 1: Rs. 500
Option 2: Rs. 1000
Option 3: Rs. 2000
Option 4: Rs. 3000
Correct Answer: Rs. 2000
Solution : Let the sum be $\text{P}$ for both cases. Time = 5 years and 4 years. Difference = 150 According to the question: By using the formula of Simple Interest: SI = $\frac{\text{P×R×T}}{100}$ where $P$ is principal, $T$ is time in years and $R$ is the rate of interest per annum. $\frac{\text{P×7.5×5}}{100}-\frac{\text{P×7.5×4}}{100}$ = 150 ⇒ $\frac{\text{7.5P}}{100}$ = 150 ⇒ $\text{P}$ = Rs. 2000 Hence, the correct answer is Rs. 2000.
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