Exercise: 6-C
Assertion- Reason Questions
Q1: Assertion (A): The population of a village is 8000. Out of these, 80% are literate and of these literate people, 40% are women, The ratio of the number of literate women to the number of illiterate is 8 : 5.
Reason (R): Percentage can be converted into ratios and vice-versa.
Step-by-step verification of Assertion:
Step 1: Total population = 8000
Step 2: Literate = 80% of 8000 =
\[
\frac{80}{100} \times 8000 = 6400
\]Step 3: Literate women = 40% of 6400 =
\[
\frac{40}{100} \times 6400 = 2560
\]Step 4: Illiterate people = 8000 – 6400 = 1600
Step 5: Ratio of literate women to illiterate =
\[
\frac{2560}{1600} = \frac{16}{10} = \frac{8}{5}
\]✅ So the Assertion (A) is TRUE
Now check the Reason (R):
“Percentage can be converted into ratios and vice-versa.”
✅ This is a general mathematical fact.
For example, 80% = 80 : 100 = 4 : 5. So Reason is also TRUE.
But is the Reason the correct explanation?
❌ No — the reason talks about conversion, but the assertion is about a specific population ratio. So Reason is not the explanation of Assertion.
Answer: b. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
Q2: Assertion (A): If 240 is increased by 5%, it becomes 252.
Reason (R): If a value p is increased by x%, then the new values becomes \(\left(1+\frac{x}{100}\right)\)p.
Step-by-step verification of Assertion:
Step 1: Increase 240 by 5%
\[
\text{New value} = \left(1 + \frac{5}{100}\right) \times 240 = \left(1 + 0.05\right) \times 240 = 1.05 \times 240 \\
= 252
\]✅ So, the Assertion (A) is TRUE
Now verify the Reason:
Step 2: The formula for increasing a number \(p\) by \(x\%\) is:
\[
\text{New value} = \left(1 + \frac{x}{100}\right) \times p
\]✅ This is a standard percentage increase formula, hence Reason is TRUE.
Step 3:The Reason clearly explains why Assertion (A) is true — it is the exact method used to calculate the increased value.
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
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