6 men and 8 boys can finish a piece of work in 10 days. While 26 men and 48 boys can finish the work in 2 days. In how many days a group of 15 men and 20 boys do that work?
Answer & explanation
Correct answer: option 3
let M denotes the work done by a man in 1 day and B denotes the work done by a boy in 1 day.
total work = efficiency × number of days
Now, 6 men and 8 boys do the work in 10 days , total work = 10(6M+8B)
Similarly, 26 men and 48 boys do the work in 2 days ,
total work = 2(26M+48B)
we get , 10(6M+8B) = 2(26M+48B)
60M + 80B = 52M + 96B
1M = 2B
Thus, if we say 15 men and 20 boys, we means; = 30B + 20B = 50B.
Now, (6M + 8B) do the work in 10 days.
(12B + 8B) do the work in 10 days.
20B do the work in 10 days.
1B do the work in 10×20 = 200 days.
50B will do the work in \(\frac{200}{50}\) = 4 days.