Question

3 men and 4 boys can do a piece of work in 14 days while 4 men and 6 boys
can do it in 10 days. How long would it to take 1 boy to finish the work.

Answer 1

I hope it will help you

Answer 2

Answer :

one boy can do work in 140 days

Step-by-step explanation :

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

$\text{Then, one man's 1 day work = }\frac{1}{x}\\\\\text{And, one boy's 1 day's work = }\frac{1}{y}\\\\\text{(3 men's 1 day's work) + (4 boy's 1 day's work) = }\frac{1}{14}\\\\\implies \frac{3}{x}+\frac{4}{y}=\frac{1}{14}\\\\\implies 3\cdot u +4\cdot v=\frac{1}{14}.......where\frac{1}{x}=u,\frac{1}{y}=v\\\\\implies 3\cdot u +4\cdot v=\frac{1}{14}...........(1)$

$\text{Again, (4 men's 1 day's work) + (6 boy's 1 day's work) = }\frac{1}{10}\\\\\implies \frac{4}{x}+\frac{6}{y}=\frac{1}{10}\\\\\implies 4\cdot u +6\cdot v=\frac{1}{10}..........(2)$

Now, (1) and (2) can be reduced into :  

42·u + 56·v = 1 ............(1)

40·u + 60·v = 1.............(2)

then by elimination method,

40 × (42·u + 56·v = 1)  - 42 × (40·u + 60·v = 1)

1680·u - 1680·u + 2240·v - 2520 v  = 40 - 42

280·v = 2     

⇒ y = 140 days

Therefore, one boy can do work in 140 days