Multiple choice

10 boys and 15 girls together can complete a piece of work in 6 days. It takes 100 days for 1 girl alone to complete the same work. How many days will be required for 1 boy alone to complete the same work?

  1. 570 days

  2. 680 days

  3. 600 days

  4. 545 days

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

1 girl takes 100 days, so 1 girl's work rate is 1/100 per day. 10 boys + 15 girls take 6 days, so their combined rate is 1/6 per day. 15 girls' rate is 15/100 = 3/20. 10 boys' rate = 1/6 - 3/20 = 10/60 - 9/60 = 1/60. Thus, 1 boy's rate = 1/600, meaning 1 boy takes 600 days.

AI explanation

Let the work done by 1 boy in 1 day be x, so 1 girl's 1 day work is 1/100. The equation for the combined work is 10x + 15/100 = 1/6. Solving for x gives 10x = 1/6 - 3/20 = 1/60, which means x = 1/600. Therefore, 1 boy alone will complete the work in 600 days.

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