Question

4 men or 6 women complete a job in 30 days.
How much time will -12 women and 2 men
take to complete the same work.


give complete explanation
​

Answer 1

Answer :-

12 men and 2 men can complete the same work in 12 days.

Solution :-

4 men or women complete a job in 30 days

So Work done by 4 men = Work done by 6 women

Multiply by 2 one both sides

Work done by 8 men = Work done 12 women --- eq(1)

Work done by 12 women and 2 men = 8 men + 2 men = 10 men

[From eq(1)]

So work done by 12 women and 2 men = Work done by 10 men --eq(2)

Given

4 men can complete a job in = 30 days

1 men can complete a job in = (4 * 30) days = 120 days

10 men can complete a job in = 120/10 = 12 days

i.e, 12 women and 2 men can complete a job in = 12 days

[From eq(2)]

Therefore 12 men and 2 men can complete the same work in 12 days.

Answer 2

SOLUTION:-

Given:

CASE 1️⃣

4 men or 6 women complete a job in 30 days.

So,

Required man- days & women- days

=) 4× 30 = 120 men-days

=) 6× 30= 180 women - days

Therefore,

One man-days:

$= > \frac{180}{120} \\ \\ = > 1.5 \: women \: days.$

CASE 2️⃣

12 women and 2 men are the same work as:

$= > \frac{12}{1.5} + 2 \\ \\ = > \frac{12 + 3}{1.5} \\ \\ = > \frac{15 \times 10}{1.5 \times 10} \\ \\ = > \frac{150}{15} \\ \\ = > 10 \: men$

So,

The work can be done in 120 man-days by 10 men:

=) 120/10

=) 12 days.

Therefore,

12 days take to completed the work.

Hope it helps ☺️