- QUESTION
Given below are two statements:
Statement 1:
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 Il is true
Explanation
(A)
=Statement I:
Given that Ram and Shyam can finish a task by working together in 6 days, and Shyam can finish the task alone in 8 days. From this, we can calculate their individual rates of work. Let’s denote the rate of work of Ram as R (in tasks per day) and the rate of work of Shyam as S (in tasks per day). Then
1/(R + S) = 6Ram and Shyam together
1/8 = 8(Shyam alone)
From the first equation, we can find R + S = 1/6 and from the second equation, S = 1/8
Substituting the value of S in the first equation:
R + 1/8 = 1/6
R = 1/6 – 1/8 = 4/24 – 3/24 = 1/24
So, Ram alone will take 24 days to finish the task. Statement I is true.
Statement II:
Given that 6 persons working 8 hours a day earn $8,400 per week, and we need to finc out the earnings of 9 persons working 6 hours a day per week. This is a straightforward application of the principle of proportionality. The total amount earned is directly proportional to the number of persons and the number of hours worked per day
Let’s denote the earnings of 9 persons working 6 hours a day per week as E.
Then,
6 persons x8 hours/dayx8400/9 persons x6 hours/day=E
After canceling out common terms, we find that E=9450
So, Statement II is true.
Therefore, the correct answer is A) Both Statement I and Statement II are true.
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