Question

3 men and 4 boys can do a piece of work in 14 days, while 4 men and 6 boys do the same work in 10 days. How long would it take one man to finish the same work

Answer 1

Let one man's one day's work be x

Let one boy's one day's work be y

According to first condition,

3x+4y=141​     .......Equation 1

According to second condition,

4x+6Y=101​     .......Equation 2

Multiplying Equation 1 by 4 and Equation 2 by 3,

12x+16y=144​     .....Equation 3

12x+18y=103​     .....Equation 4

Now solving Equation 3 and 4 simultaneously by subtracting Equation 3 by Equation 4,

we get,

∴−2y=144​−103​

∴−2y=14040−42​

∴y=1401​

Putting the value of y in equation 1, we get,

3x+1404​=141​

∴x=701​

Hence one man's one day  work is 1/70

∴ one man completes the whole work in 70 days.