Multiple choice

$2$ men and $3$ boys together can do a piece of work in $8$ days. The same work is done in $6$ days by $3$ men and $2$ boys together. How long would $1$ boy alone or $1$ man alone take to complete the work.

  1. One boy alone can do a piece of work in $130$ days

    and one man alone can do a piece of work in $160$ days
  2. One boy alone can do a piece of work in $90$ days

    and one man alone can do a piece of work in $70$ days
  3. One boy alone can do a piece of work in $120$ days

    and one man alone can do a piece of work in $20$ days
  4. One boy alone can do a piece of work in $160$ days

    and one man alone can do a piece of work in $12$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M and B be the daily work of a man and a boy. 8(2M + 3B) = 1 => 16M + 24B = 1. 6(3M + 2B) = 1 => 18M + 12B = 1. Solving the system: multiply second by 2: 36M + 24B = 2. Subtracting first: 20M = 1 => M = 1/20. Then 12B = 1 - 18(1/20) = 1 - 0.9 = 0.1 => B = 1/120. Man takes 20 days, boy takes 120 days.

AI explanation

Let a man's daily work be M and a boy's daily work be B. The given statements establish the equations 2M + 3B = 1/8 and 3M + 2B = 1/6. Solving this system of linear equations yields M = 1/20 and B = 1/120. Consequently, one man alone completes the work in 20 days and one boy alone takes 120 days.

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