Multiple choice

5 men and 2 boys started working together to complete a work which they can complete in 10 days. After 6 days, they were joined by 4 more boys. In how many days will the remaining work be completed? Statements: A. Working together, a man and a boy can complete the whole work in 40 days. B. Remaining work is done by 5 men and 6 boys. C. Working alone, 6 men could have completed half of the remaining work in 2 days.

  1. Only A is sufficient

  2. Only B is sufficient

  3. Only C is sufficient

  4. Either A or C is sufficient

  5. Either B or C is sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A gives the work rate of 1 man and 1 boy. Statement C gives the work rate of 6 men. Both allow calculating the individual rates of men and boys, which is sufficient to determine the remaining work time. Statement B is just a description of the remaining work.

AI explanation

We need to find the ratio of efficiency between a man and a boy, let it be M is to B. The equation for the total work based on the initial team is (5M + 2B) times 10 days. Statement A gives the combined rate of one man and one boy as 1 divided by 40, yielding the equation M + B equals Total Work divided by 40, which can be solved with the first equation to find the exact ratio. Statement C gives the rate of six men as one fourth of the remaining work per day, which calculates to 6M equals Total Work divided by 40, providing another valid ratio. Therefore, either statement A or statement C is sufficient to solve the problem.

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