A work can be completed by 8 men or 12 women in 25 days. 10 men and 5 women willcomplete the same work in

Given:

8 men can complete the work in 25 days.

12 women can complete the same work in 25 days.

Formula Used:

M₁ × D₁ = M₂ × D₂ (when work is constant)

Let the work done by 1 man in 1 day be 'm' units.

Let the work done by 1 woman in 1 day be 'w' units.

Total work = Number of men × work per man per day × Number of days

Total work = Number of women × work per woman per day × Number of days

Calculation:

Work done by 8 men in 25 days = 8m × 25 = 200m units

Work done by 12 women in 25 days = 12w × 25 = 300w units

Since the work is the same:

200m = 300w

⇒ 2m = 3w

⇒ w = (2/3)m

Work of 5 women = 5 × w = 5 × (2/3)m = (10/3)m

So, 10 men and 5 women are equivalent to 10m + (10/3)m men.

Equivalent men = (30/3)m + (10/3)m = (40/3)m

Let the number of days taken by 10 men and 5 women be 'D' days.

Using the MDH formula:

M₁ × D₁ = M₂ × D₂

Here, M₁ = 8 men, D₁ = 25 days

M₂ = (40/3) equivalent men, D₂ = D days

8 × 25 = (40/3) × D

200 = (40/3) × D

600 = 40 × D

D = 600 / 40

D = 15

∴ 10 men and 5 women will complete the same work in 15 days.