Multiple choice

A man a woman and a boy can complete a job in $3, 4$ and $12$ days respectively. How many boys must assist 1 man and 1 woman to complete the job in $\displaystyle \frac{1}{4}$ of a day?

  1. $1$
  2. $4$
  3. $19$
  4. $41$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rates: Man = 1/3, Woman = 1/4, Boy = 1/12. Total work needed in 1/4 day is 1 unit. 1 man + 1 woman in 1/4 day = (1/3 + 1/4) * 1/4 = (7/12) * 1/4 = 7/48. Remaining work = 1 - 7/48 = 41/48. Boys needed = (41/48) / (1/12 * 1/4) = (41/48) / (1/48) = 41.

AI explanation

Taking the total work as the least common multiple of 3, 4 and 12 gives 12 units, making the daily capacities of one man, one woman and one boy equal to 4, 3 and 1 units respectively. The required work for one-fourth of a day is 12 multiplied by 4, which is 48 units per day. One man and one woman provide 7 units daily, leaving 41 units to be provided by the boys, meaning 41 boys must assist them.

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