Multiple choice

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 persons working 6 hours a day will earn ₹9,450 per week. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: 1/R + 1/8 = 1/6, so 1/R = 1/6 - 1/8 = 1/24, R = 24. True. Statement II: (6*8)/8400 = (9*6)/X, so 48/8400 = 54/X, X = 54 * 8400 / 48 = 9450. True.

AI explanation

For Statement I, Ram and Shyam have a combined one-day work of 1/6 and Shyam's one-day work is 1/8, so Ram's one-day work is 1/6 minus 1/8, which equals 1/24; therefore, Ram alone takes 24 days, making Statement I true. For Statement II, the earnings are proportional to the total person-hours worked, so the ratio of earnings is (9 persons times 6 hours) to (6 persons times 8 hours), which is 54 to 48 or 9 to 8. Multiplying this ratio by the base earnings of Rs. 8,400 results in Rs. 9,450, making Statement II true. Therefore, both Statement I and Statement II are true.

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