A work is done by 3 males in 16 days and the same work is done by 6 females in 16 days. If 12 males and 8 females work together, then they completed the work in how many days?

Given:

A work is done by 3 males in 16 days and the same work is done by 6 females in 16 days.

Formula used:

Work done per day by 1 male = \(\dfrac{1}{3 \times 16}\)

Work done per day by 1 female = \(\dfrac{1}{6 \times 16}\)

Calculation:

Work done per day by 1 male = \(\dfrac{1}{48}\)

Work done per day by 1 female = \(\dfrac{1}{96}\)

Work done per day by 12 males and 8 females:

= 12 × \(\dfrac{1}{48}\) + 8 × \(\dfrac{1}{96}\)

⇒ = \(\dfrac{12}{48}\) + \(\dfrac{8}{96}\)

⇒ = \(\dfrac{1}{4}\) + \(\dfrac{1}{12}\)

⇒ = \(\dfrac{3}{12}\) + \(\dfrac{1}{12}\)

⇒ = \(\dfrac{4}{12}\)

⇒ = \(\dfrac{1}{3}\)

Number of days to complete the work = \(\dfrac{1}{\dfrac{1}{3}}\)

⇒ = 3 days

∴ The correct answer is option 4.