Question

3 Mens 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 take for 7 men and 10 boys to do the work.​

Answer 1

Answer:

$\frac{1}{70} \: or \: 70$ days

Step-by-step explanation:

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

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

According to first condition

$3x + 4y = \frac{1}{14}$

According to second condition,

$4x + 6y = \frac{1}{10}$

Multiplying Equation 1 by 4 and Equation 2 by 3,

$12x + 16y = \frac{4}{14} \\ equation3$

$12x + 18y = \frac{3}{10} \\ equation \: 4$

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

we get,

$- 2y = \frac{40 - 42}{140}$

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

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

$3x + \frac{4}{140} = \frac{1}{14}$

$x = \frac{1}{70}$

Hence one man's one day work is

$\frac{1}{70}$

∴ one man completes the whole work in 70 days