Answer:

12 days

Step-by-step explanation:

LET the time taken by 1 women alone to do the work =x days and the time taken by 1 men to do the work =y days.

Then, work done by 1 women in 1 day =

x

1

and work done by 1 men in 1 day =

y

1

Therefore, work done by 2 men in 1 day =

x

2

and work done by 7 boys in 1 day =

y

7

According to the question,

Work done by 2 men and 7 boys in 1 day =

4

1

Thus,

x

2

+

y

7

=

4

1

....(i)

Similarly, work done by 4 men in 1 day =

x

4

and work done by 4 boys in 1 day =

y

4

Work done by 4 men and 4 boys in 1 day =

3

1

x

4

+

y

4

=

3

1

....(ii)

Putting

x

1

=pand

y

1

=q in equation (i) and (ii), we get,

2p+7q=

4

1

and4p+4q=

3

1

or,2p+7q=

4

1

=>8p+28q=1

=>p=

8

1−28q

....(III)

Also,4p+4q=

3

1

=>12p+12q=1....(iv)

Substituting equation (iii) in equation (iv), we get,

12p+12q=1

=>12(

8

1−28q

)+12q=1

=>

2

3−84q

+12q=1

=>3−84q+24q=2

=>−60q=−1

=>q=

60

1

Substituting q=

60

1

in equation (iii), we get,

p=

8

1−28q

=>p=

8

1−28×

60

1

=>p=

8

1−

15

7

=>p=

15

8

×

8

1

=

15

1

p=

x

1

=

15

1

=>x=15

q=

y

1

=

60

1

=>y=60

Thus, time taken by 1 man alone to do the work =x=15 days and time taken by 1 BOY alone to do the work =y=60 days

Work done by 1 man and 1 boy in 1 day

15

1

+

60

1

=

60

5

=

12

1

Time taken by 1 man and 1 boy to do the work =12 days.