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Question
A sum of money at simple interest amounts to TK. 5600 in 2 years and Tk. 6500 in 5 years at the rate of -
4%
3%
5%
6%
ANSWER : 4
Descrption
<p style="margin-left:0px;">To find the rate of simple interest, we can use the formula:</p><p style="margin-left:0px;">Simple Interest (SI) = (Principal * Rate * Time) / 100</p><p style="margin-left:0px;">We are given two different scenarios:</p><ol><li>The money amounts to Tk. 5600 in 2 years.</li><li>The money amounts to Tk. 6500 in 5 years.</li></ol><p style="margin-left:0px;">Let's use the first scenario to calculate the rate:</p><p style="margin-left:0px;">SI = (Principal * Rate * Time) / 100</p><p style="margin-left:0px;">5600 = (Principal * Rate * 2) / 100</p><p style="margin-left:0px;">Now, rearrange the formula to solve for the rate (R):</p><p style="margin-left:0px;">Rate (R) = (SI * 100) / (Principal * Time)</p><p style="margin-left:0px;">Rate (R) = (5600 * 100) / (Principal * 2)</p><p style="margin-left:0px;">Now, let's use the second scenario to calculate the rate:</p><p style="margin-left:0px;">SI = (Principal * Rate * Time) / 100</p><p style="margin-left:0px;">6500 = (Principal * Rate * 5) / 100</p><p style="margin-left:0px;">Again, rearrange the formula to solve for the rate (R):</p><p style="margin-left:0px;">Rate (R) = (SI * 100) / (Principal * Time)</p><p style="margin-left:0px;">Rate (R) = (6500 * 100) / (Principal * 5)</p><p style="margin-left:0px;">Now, let's compare the rates from both scenarios:</p><p style="margin-left:0px;">Rate in the first scenario (R1) = (5600 * 100) / (Principal * 2) Rate in the second scenario (R2) = (6500 * 100) / (Principal * 5)</p><p style="margin-left:0px;">Since both scenarios involve the same principal amount, we can compare the rates:</p><p style="margin-left:0px;">R1 / R2 = [(5600 * 100) / (Principal * 2)] / [(6500 * 100) / (Principal * 5)]</p><p style="margin-left:0px;">R1 / R2 = (5600 * 100 * 5) / (6500 * 100 * 2)</p><p style="margin-left:0px;">R1 / R2 = 28000 / 13000</p><p style="margin-left:0px;">R1 / R2 = 2.1538 (approximately)</p><p style="margin-left:0px;">So, the rate of interest is approximately 2.1538 times higher in the second scenario compared to the first scenario.</p><p style="margin-left:0px;">Now, let's calculate the rate in the second scenario (R2):</p><p style="margin-left:0px;">R2 = (Rate in the first scenario, R1) * 2.1538</p><p style="margin-left:0px;">R2 ≈ 6% (approximately)</p><p style="margin-left:0px;">Therefore, the rate of interest is approximately 6%.</p>
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