Multiple choice

If 2 boys and 5 girls complete a piece of work in 3 days, while 6 boys and 6 girls complete the same work in 2 days, then how many days will 1 girl alone take to finish the work?

  1. 36 days

  2. 18 days

  3. 12 days

  4. 10 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B be the work done by a boy per day and G be the work done by a girl per day. We have 2B + 5G = 1/3 and 6B + 6G = 1/2. Multiplying the first equation by 3 gives 6B + 15G = 1. Subtracting the second equation (6B + 6G = 1/2) from this gives 9G = 1/2, so G = 1/18. One girl takes 18 days.

AI explanation

Using the Least Common Multiple method, let the total work be 12 units based on the given days. Two boys and five girls complete 4 units per day, while six boys and six girls complete 6 units per day. By dividing the second equation by 3 to get 2 boys and 2 girls equaling 2 units per day, and subtracting this from the first equation, we find 3 girls equal 2 units per day. This means one girl does 2/3 units per day, so dividing the total 12 units by 2/3 gives 18 days for one girl to finish the work alone.

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