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The difference between the compound interest and the simple interest on a principal sum of ₹24,000 in 2 years at same rate of interest is ₹260. The ra
Question

The difference between the compound interest and the simple interest on a principal sum of ₹24,000 in 2 years at same rate of interest is ₹260. The rate of interest is:

A.

7%

B.

10%

C.

8%

D.

5%

Correct option is B

Given:
Principal (P) = ₹24,000
Time (T) = 2 years
Difference between Compound Interest (CI) and Simple Interest (SI) = ₹260
Formula Used:
The formula for the difference between CI and SI for 2 years is:
Difference=P×(R100)2\text{Difference} = P \times \left( \frac{R}{100} \right)^2​​
Where:
P = Principal
R = Rate of Interest
Solution:
Using the formula for the difference between CI and SI:

260=24000×(R100)2260 = 24000 \times \left( \frac{R}{100} \right)^2​​

260=24000×R210000260 = 24000 \times \frac{R^2}{10000}​​

260=2.4×R2​260 = 2.4 \times R^2​​

R2=2602.4=108.33R^2 = \frac{260}{2.4} = 108.33​​

R=108.3310.4R = \sqrt{108.33} \approx 10.4​​

Thus, the rate of interest R is approximately 10%

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