Question

2 men and 7 boys can do a work in 4 days.the same work is done in 3 days by 4 men and 4 boys.how long would it take for one man and one boy to do it alone??

Answer 1

Answer:

Step-by-step explanation: let no. of men be =x

let no. of  boys=y

first equation-2x+7y=4

second equation=4x+4y=3

$2x+7y=4\\2x=4-7y\\\frac{4-7y}{2} =x$

insert value of x in second equation

$\frac{4-7y}{2} +4y=3\\\frac{4-7y+8y}{2} =3\\\\\frac{4+y}{2} =3\\\frac{4+y}{} =6\\ y=2$

4-7y/2=x

4-14/2=x

10/2=x

5=x

x+y=2+5=7

it would take 7 days

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Answer 2

Answer:

given  

2 men and 7 boys can do a work in 4 days

the same work is done in 3 days by 4 men and 4 boys.                          

let the no of men and no of boys be x and y respectively

2x + 7y = 4     --------- 1

4x + 4y = 3      --------- 2

x + y=  ?

solving the simultaneous linear equation

multiply the equation no 1 by 2

so 4x + 14 y = 8

    4x + 4y = 3      subtraction

---------------------------

           10y = 5

            y = 1/2

substituting   y in equation 1

2x + 7y =4

2x = 4- 7/2

2x = 1/2

x= 1/4

x=1/4 and y= 1/2

therefore

x + y=  1/4 +1/2

      = 3/4 days  (answer )

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