Exercise: 8-E
ASSERTION-REASON QUESTIONS
Q1: Assertion (A): Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest annum.
Reason (R): \(S.I.\ =\ \frac{PRT}{100}\).
Step 1: Analyze the Assertion (A):
Compound interest includes interest on the interest of previous years, while simple interest is calculated only on the principal.
So, for the same principal, time, and rate:
\[
\text{Compound Interest} \geq \text{Simple Interest}
\]
Hence, Assertion (A) is true.
Step 2: Analyze the Reason (R):
\[
\text{Simple Interest} = \frac{P \times R \times T}{100}
\]
This is the correct formula for simple interest. So, Reason (R) is also true.
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Q2: Assertion (A): The interest on a sum of ₹P for n years at r% per annum is given by the formula \(P\left(1+\frac{rn}{100}\right)\).
Reason (R): \(Compound\ Interest\ \left(Cl\right)=\ Final\ amount\ -\ Original\ amount\)
Step 1: Analyze Assertion (A):
The formula \(P\left(1+\frac{rn}{100}\right)\) gives the amount under simple interest, not the interest itself.
The interest under simple interest is:
\[
SI = \frac{P \times R \times T}{100}
\]
So, Assertion (A) is false — it incorrectly states the amount formula as the formula for interest.
Step 2: Analyze Reason (R):
\[
CI = \text{Amount} – \text{Principal}
\]
This is the correct definition of compound interest.
So, Reason (R) is true.
Answer: d. Assertion (A) is false but Reason (R) is true.
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