Multiple choice

If $12$ men and $16$ boys can do piece of work in $5$ days and if $13$ men and $24$ boys can do it in $4$ days, how long will $7$ men and $10$ boys take to do it ?

  1. $ 3\dfrac{2}{3} $ Days
  2. $ 8 \dfrac{1}{3} $ Days
  3. $ 4 \dfrac{5}{3} $ Days
  4. $ 9 \dfrac{1}{3} $ Days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be work of one man, B be work of one boy. 5(12M + 16B) = 1. 4(13M + 24B) = 1. 60M + 80B = 52M + 96B => 8M = 16B => M = 2B. Substitute: 5(12(2B) + 16B) = 5(40B) = 1 => 200B = 1. Work of 7M + 10B = 7(2B) + 10B = 24B. Time = 200B / 24B = 200/24 = 25/3 = 8 1/3 days.