Question

Given below are two statements:
Statement I: Ram and Shyam can finish a task by working together in 6 days. If Shyam can finish the task by working alone in 8 days, then Ram alone will take 24 days to finish it.
Statement II: If 6 persons working 8 hours a day earn 8,400 per week, then 9 person working 6 hours a day will eam 9,450 per week.
In the light of the above statements, choose the correct answer from the options given below:

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is A

In Statement I, Ram and Shyam's combined rate of work is \( \frac{1}{6} \), and Shyam's rate of work is \( \frac{1}{8} \). Therefore, Ram’s rate is \[ \frac{1}{6} - \frac{1}{8} = \frac{1}{24}, \] meaning Ram alone will take 24 days to finish the task, which is *true*.

In Statement II, the weekly earnings should be *proportional* to both the number of *people* and the *hours worked*. The earnings for 9 persons working 6 hours a day are actually less than stated, so Statement II is false.