Question

8 men and 12 boys can finish a work in 10 days while 6 men and 8 boys can finish it in 14 day.Find the time taken by one màn and one boy alone to finish the work.​

Answer 1

One man alone can finish the work in 140 days and one boy alone can finish the work in 280 days.    

Step-by-step explanation:

Given:

Here 8 men and 12 boys can finish a work in 10 days while 6 men and 8 boys can finish it in 14 day.

Suppose that one man alone can finish the work in x days and one boy alone can finish it in y days. Then,

One man's one day's work = $\frac{1}{x}$

One boy's one day's work = $\frac{1}{y}$

∴ Eight men's one day's work = $\frac{8}{x}$

12 boy's one day's work = $\frac{12}{y}$

Since 8 men and 12 boys can finish the work in 10 days,

$10(\frac{8}{x} +\frac{12}{y}) = 1$

⇒ $(\frac{80}{x} +\frac{120}{y}) = 1$                        [1]

Again, 6 men and 8 boys can finish the work in 14 days.

$14(\frac{6}{x} +\frac{8}{y}) = 1$

⇒ $(\frac{84}{x} +\frac{112}{y}) = 1$                        [2]

Putting $\frac{1}{x}=u$  and $\frac{1}{y}=v$ in equations (1) and (2), we get

80u + 120v − 1 = 0  

84u + 112v - 1 = 0

By using cross-multiplication method, we have

$\frac{u}{-112+120} =\frac{-v}{-80+84} =\frac{1}{80\times 112-120\times 84}$

$\frac{u}{-8} =\frac{-v}{4} =\frac{1}{-1120}$

$\frac{u}{-8} =\frac{1}{-1120}$

$u = \frac{-8}{-1120}$

$u=\frac{1}{140}$

And $\frac{-v}{4} =\frac{1}{-1120}$

$v=\frac{-4}{-1120}$

$v=\frac{1}{280}$

Now Substituting $u=\frac{1}{x}$, we get

$u=\frac{1}{140} \Rightarrow \frac{1}{x}=\frac{1}{140}\Rightarrow x = 140$

$v=\frac{1}{280} \Rightarrow \frac{1}{y}=\frac{1}{280}\Rightarrow y = 280$

Thus, one man alone can finish the work in 140 days and one boy alone can finish the work in 280 days    

 

Answer 2

Dear Student,

◆ Answer -

93.33 days

● Explanation -

Let x and y be part of the work 1 man and 1 boy can finish in 1 day respectively.

8x + 12y = 1/10 ...(1)

6x + 8y = 1/14 ...(2)

Solving (1) & (2),

x = 1/140

y = 1/280

So the days taken by 1 man and 1 boy alone to complete the work -

1/140 + 1/280 = 1/t

3/280 = 1/t

1/t = 3/280

t = 93.33 days

Hence, 93.33 days taken by 1 man and 1 boy alone to complete the work.

Thanks dear. Hope this helps you...