Exercise: 11-B
Assertion- Reason Questions
Q1: Assertion (A): If a man can complete a work in 10 days, then he will complete \(\frac{1}{5}\) of the work in 2 days.
Reason (R): If a person can complete a work in n days, then in 1 day he does \(\frac{1}{n}\) of the work.
i. Analyze the Reason (R)
Step 1: If a person can do a work in \(n\) days, then in 1 day he does \(\frac{1}{n}\) of the work.
⇒ If \(n = 10\), 1 day’s work = \(\frac{1}{10}\)
✔️ So, Reason (R) is true.
ii. Analyze the Assertion (A)
Step 2: Man can complete a work in 10 days ⇒ 1 day’s work = \(\frac{1}{10}\)
2 days’ work = \(2 \times \frac{1}{10} = \frac{2}{10} = \frac{1}{5}\)
✔️ So, Assertion (A) is also true.
iii. Is Reason the correct explanation of Assertion?
Step 3: Yes, the Reason explains why the man does \(\frac{1}{5}\) of the work in 2 days.
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Q2: Assertion (A): Anish can do \(\frac{1}{3}\) of a work in 5 days. Brijesh can do \(\frac{1}{2}\) of the same work in 6 days. Together they will take 6 days to complete the work.
Reason (R): Number of men to complete a work and time taken by them vary inversely with each other.
i. Analyze Anish’s and Brijesh’s work rates
Step 1: Anish does \(\frac{1}{3}\) of work in 5 days ⇒ Full work in \(5 \times 3 = 15\) days ⇒ 1 day’s work = \(\frac{1}{15}\)
Step 2: Brijesh does \(\frac{1}{2}\) of work in 6 days ⇒ Full work in \(6 \times 2 = 12\) days ⇒ 1 day’s work = \(\frac{1}{12}\)
ii. Calculate total work they can do together in one day
Step 3: Together’s 1 day work = \(\frac{1}{15} + \frac{1}{12} = \frac{4 + 5}{60} = \frac{9}{60} = \frac{3}{20}\)
⇒ Time to finish the full work = \(\frac{1}{\frac{3}{20}} = \frac{20}{3} ≈ 6.67\) days
Conclusion: Assertion says they will finish in 6 days, but actual time is approx 6.67 days.
❌ So, Assertion (A) is false.
iii. Analyze the Reason (R)
Step 4: Reason (R): “Number of men to complete a work and time taken by them vary inversely with each other.”
✔️ This is a correct principle in work-time problems. So, Reason (R) is true.
Answer: d. Assertion (A) is false but Reason (R) is true.
