Multiple choice

$8$ men and $12$ boys can finish a piece of work in $10$ days, while $6$ men and $8$ boys can finish it in $ 14 $ days. Find the time taken by one man alone and that by one boy alone to finish that work.

  1. Man: $160$ days. Boy : $190$ days
  2. Man: $140$ days. Boy : $280$ days
  3. Man: $240$ days. Boy : $150 $days
  4. Man: $260$ days. Boy : $200$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be man's rate, B be boy's rate. 8M + 12B = 1/10; 6M + 8B = 1/14. Solving this system: 24M + 36B = 3/10; 24M + 32B = 4/14 = 2/7. Subtracting: 4B = 3/10 - 2/7 = (21-20)/70 = 1/70. B = 1/280. 6M + 8(1/280) = 1/14 => 6M + 1/35 = 1/14 => 6M = 5/70 - 2/70 = 3/70. M = 1/140. Times are 140 and 280.

AI explanation

Let m be the daily work of a man and b be the daily work of a boy, giving the equations 80m + 120b = 1 and 84m + 112b = 1 based on the total work. Equating the adjusted equations 560m + 840b = 7 and 560m + 746.67b = 6.67 reveals a slight calculation discrepancy in the provided choices, so we look at the ratio from the exact equations. Solving the exact equations yields m = 1/140 and b = 1/280, meaning the man alone takes 140 days and the boy alone takes 280 days.

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