Question

7 men and 8 boy can do a piece of work in 2 days. 4men and 12 boys can do 29/56 of the same work in 1 day. In how many days will 1 man do this work?

Answer 1

hey mate
here's the solution

Answer 2

Answer: 1 man will do this work in 28 days.

Step-by-step explanation:

Since we have given that

7 men and 8 boys can do a piece of work in 2 days.

4 men and 12 boys can do $\frac{29}{56}$ of work in 1 day.

so, by using "Time and work":

$\frac{(7M\times+8B)\times 2}{1}=\frac{(4M\times 12B)\tiems 1}{\frac{29}{56}}\\\\(7M+8B)=\frac{4M+12B}{29}\times \frac{56}{2}\\\\29(7M+8B)=28(4M+12B)\\\\203M+232B=112M+336B\\\\203M-112M=336B-232B\\\\91M=104B\\\\B=\frac{91}{104}M=\frac{7}{8}M$

So, Number of days 1 man will do this work is given by

$(7M+8B)\times 2=1M\times x\\\\(7M+8\times \frac{7M}{8})\times 8=1M\times x\\\\(7M+7M)\times 2=1M\times x\\\\14M\times 2=1M\times x\\\\x=28\ days$

Hence, 1 man will do this work in 28 days.