Multiple choice

Choose the most appropriate option. Two men and seven boys can do a work in $14$ days. Three men and eight boys can do the same work in $11$ days. Further eight men and six boys can do three times the amount of this work in:

  1. $18$ days
  2. $30$ days
  3. $24$ days
  4. $21$ days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M be the work of a man and B be the work of a boy per day. From the equations 14(2M + 7B) = W and 11(3M + 8B) = W, we find 28M + 98B = 33M + 88B, which simplifies to 5M = 10B or M = 2B. Substituting M = 2B into the first equation, 14(4B + 7B) = 154B = W. For 8M + 6B, we have 8(2B) + 6B = 22B. The time required for 3W is (3 * 154B) / 22B = 21 days.

AI explanation

From the given data, 14 times (2 men plus 7 boys) equals 11 times (3 men plus 8 boys), leading to 28m plus 98b equals 33m plus 88b. Simplifying this gives 5m equals 10b, meaning 1 man does the work of 2 boys. Therefore, the original work requires 11 days of 14 boys, totaling 154 boy-days of effort. To complete three times this amount, 8 men and 6 boys act as 22 boys, requiring 3 multiplied by 154 divided by 22 days, which equals 21 days.

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