Question

. 3 men and 4 boys can do a piece of work in 14
days, while 4 men and 6 boys do the same work
in 10 days. How long would it take one man to
finish the same work?​

Answer 1

Answer:

It will take 70 days for one man to complete work alone .

Answer 2

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= 1/14 (...Equation 1)

According to second condition,

4x+6Y= 3/10 (...Equation 2)

Multiplying Equation 1 by 4 and Equation 2 by 3,

12x+16y= 4/14 (...Equation 3)

12x+18y= 3/10 (...Equation 4)

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

we get,

$∴−2y= \frac{4}{14} - \frac{3}{10}$

$∴−2y= \frac{</p><p>40−42}{140}$

$∴y= \frac{1}{140}$

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 1/70

∴ One man completes the whole work in 70 days.