Question

7 men and 8 boys can do a piece of work in 2 days.
29
4 men and 12 boys can do of the same work in
56
1 day. In how many days will 1 man do this work?
(a) 24 days
(b) 25 days
(c) 28 days
(d) 30 days​

Answer 1

Answer:

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}

56

29

of work in 1 day.

so, by using "Time and work":

\begin{gathered}\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\end{gathered}

1

(7M×+8B)×2

=

56

29

(4M×12B)\tiems1

(7M+8B)=

29

4M+12B

×

2

56

29(7M+8B)=28(4M+12B)

203M+232B=112M+336B

203M−112M=336B−232B

91M=104B

B=

104

91

M=

8

7

M

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

\begin{gathered}(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\end{gathered}

(7M+8B)×2=1M×x

(7M+8×

8

7M

)×8=1M×x

(7M+7M)×2=1M×x

14M×2=1M×x

x=28 days